M. Brown :
“A countable connected Hausdorff space ,”
Bull. Amer. Math. Soc.
59
(1953 ),
pp. 367 .
Abstract only (inside The April meeting in New York ); unpublished.
article
Abstract
BibTeX
The points are the positive integers. Neighborhoods are sets of integers \( \{a+bx\} \) where \( a \) and \( b \) are relatively prime to each other (\( x = 1, 2 \) , \( 3,\dots \) ). Let \( \{a+bx\} \) and \( \{c+dx\} \) be two neighborhoods. It is shown that \( bd \) is a limit point of both neighborhoods. Thus, the closures of any two neighborhoods have a nonvoid intersection. This is a sufficient condition that a space be connected.
@article {key37975439,
AUTHOR = {Brown, Morton},
TITLE = {A countable connected {H}ausdorff space},
JOURNAL = {Bull. Amer. Math. Soc.},
VOLUME = {59},
YEAR = {1953},
PAGES = {367},
NOTE = {Abstract only (inside \textit{The April
meeting in New York}); unpublished.},
}
M. Brown :
Continuous collections of higher dimensional
hereditarily indecomposable continua .
Ph.D. thesis ,
The University of Wisconsin, Madison ,
1958 .
Advised by R. H. Bing .
MR
2612711
People
BibTeX
@phdthesis {key2612711m,
AUTHOR = {Brown, Morton},
TITLE = {Continuous collections of higher dimensional
hereditarily indecomposable continua},
SCHOOL = {The University of Wisconsin, Madison},
YEAR = {1958},
PAGES = {40},
NOTE = {Advised by R. H. Bing. MR
2612711.},
}
M. Brown :
“Weak \( n \) -homogeneity implies weak \( (n-1) \) -homogeneity ,”
Proc. Amer. Math. Soc.
10
(1959 ),
pp. 644–647 .
MR
0107857
Zbl
0093.36604
BibTeX
@article {key0107857m,
AUTHOR = {Brown, Morton},
TITLE = {Weak \$n\$-homogeneity implies weak \$(n-1)\$-homogeneity},
JOURNAL = {Proc. Amer. Math. Soc.},
FJOURNAL = {Proceedings of the American Mathematical
Society},
VOLUME = {10},
YEAR = {1959},
PAGES = {644--647},
NOTE = {Available at
http://dx.doi.org/10.2307/2033668.
MR 21 \#6579. Zbl 0093.36604.},
ISSN = {0002-9939},
}
M. Brown :
“Some applications of an approximation theorem for inverse
limits ,”
Proc. Amer. Math. Soc.
11
(1960 ),
pp. 478–483 .
MR
0115157
Zbl
0113.37705
BibTeX
@article {key0115157m,
AUTHOR = {Brown, Morton},
TITLE = {Some applications of an approximation
theorem for inverse limits},
JOURNAL = {Proc. Amer. Math. Soc.},
FJOURNAL = {Proceedings of the American Mathematical
Society},
VOLUME = {11},
YEAR = {1960},
PAGES = {478--483},
NOTE = {Available at
http://dx.doi.org/10.2307/2034803.
MR 22 \#5959. Zbl 0113.37705.},
ISSN = {0002-9939},
}
M. Brown :
“On the inverse limit of Euclidean \( N \) -spheres ,”
Trans. Amer. Math. Soc.
96
(1960 ),
pp. 129–134 .
MR
0119182
Zbl
0136.19805
BibTeX
@article {key0119182m,
AUTHOR = {Brown, Morton},
TITLE = {On the inverse limit of {E}uclidean
\$N\$-spheres},
JOURNAL = {Trans. Amer. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical
Society},
VOLUME = {96},
YEAR = {1960},
PAGES = {129--134},
NOTE = {Available at
http://dx.doi.org/10.2307/1993488.
MR 22 \#9948. Zbl 0136.19805.},
ISSN = {0002-9947},
}
M. Brown :
“A proof of the generalized Schoenflies theorem ,”
Bull. Amer. Math. Soc.
66
(1960 ),
pp. 74–76 .
MR
0117695
Zbl
0132.20002
BibTeX
@article {key0117695m,
AUTHOR = {Brown, Morton},
TITLE = {A proof of the generalized {S}choenflies
theorem},
JOURNAL = {Bull. Amer. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {66},
YEAR = {1960},
PAGES = {74--76},
NOTE = {Available at
http://dx.doi.org/10.1090/S0002-9904-1960-10420-X.
MR 22 \#8470b. Zbl 0132.20002.},
ISSN = {0002-9904},
}
M. Brown :
“The monotone union of open \( n \) -cells is an open \( n \) -cell ,”
Proc. Amer. Math. Soc.
12
(1961 ),
pp. 812–814 .
MR
0126835
Zbl
0103.39305
BibTeX
@article {key0126835m,
AUTHOR = {Brown, Morton},
TITLE = {The monotone union of open \$n\$-cells
is an open \$n\$-cell},
JOURNAL = {Proc. Amer. Math. Soc.},
FJOURNAL = {Proceedings of the American Mathematical
Society},
VOLUME = {12},
YEAR = {1961},
PAGES = {812--814},
NOTE = {Available at
http://dx.doi.org/10.2307/2034881.
MR 23 \#A4129. Zbl 0103.39305.},
ISSN = {0002-9939},
}
M. Brown :
“Locally flat embeddings of topological manifolds ,”
pp. 83–91
in
Topology of 3-manifolds and related topics
(Univ. of Georgia Institute, 1961 ).
Prentice-Hall (Englewood Cliffs, NJ ),
1962 .
MR
0158373
Zbl
1246.57059
BibTeX
@incollection {key0158373m,
AUTHOR = {Brown, Morton},
TITLE = {Locally flat embeddings of topological
manifolds},
BOOKTITLE = {Topology of 3-manifolds and related
topics},
PUBLISHER = {Prentice-Hall},
ADDRESS = {Englewood Cliffs, NJ},
YEAR = {1962},
PAGES = {83--91},
NOTE = {(Univ. of Georgia Institute, 1961).
MR 28 \#1598. Zbl 1246.57059.},
}
M. Brown :
“A mapping theorem for untriangulated manifolds ,”
pp. 92–94
in
Topology of 3-manifolds and related topics
(Univ. of Georgia Institute, 1961 ).
Prentice-Hall (Englewood Cliffs, NJ ),
1962 .
MR
0158374
Zbl
1246.57052
BibTeX
@incollection {key0158374m,
AUTHOR = {Brown, Morton},
TITLE = {A mapping theorem for untriangulated
manifolds},
BOOKTITLE = {Topology of 3-manifolds and related
topics},
PUBLISHER = {Prentice-Hall},
ADDRESS = {Englewood Cliffs, NJ},
YEAR = {1962},
PAGES = {92--94},
NOTE = {(Univ. of Georgia Institute, 1961).
MR 28 \#1599. Zbl 1246.57052.},
}
M. Brown :
“Locally flat imbeddings of topological manifolds ,”
Ann. of Math. (2)
75
(1962 ),
pp. 331–341 .
MR
0133812
Zbl
0201.56202
BibTeX
@article {key0133812m,
AUTHOR = {Brown, Morton},
TITLE = {Locally flat imbeddings of topological
manifolds},
JOURNAL = {Ann. of Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {75},
YEAR = {1962},
PAGES = {331--341},
NOTE = {Available at
http://dx.doi.org/10.2307/1970177.
MR 24 \#A3637. Zbl 0201.56202.},
ISSN = {0003-486X},
}
M. Brown :
“On a theorem of Fisher concerning the homeomorphism group of
a manifold ,”
Michigan Math. J.
9
(1962 ),
pp. 403–405 .
MR
0150747
Zbl
0204.23901
BibTeX
@article {key0150747m,
AUTHOR = {Brown, Morton},
TITLE = {On a theorem of {F}isher concerning
the homeomorphism group of a manifold},
JOURNAL = {Michigan Math. J.},
FJOURNAL = {The Michigan Mathematical Journal},
VOLUME = {9},
YEAR = {1962},
PAGES = {403--405},
NOTE = {Available at
http://dx.doi.org/10.1307/mmj/1028998777.
MR 27 \#734. Zbl 0204.23901.},
ISSN = {0026-2285},
}
M. Brown and H. Gluck :
“Stable structures on manifolds ,”
Bull. Amer. Math. Soc.
69
(1963 ),
pp. 51–58 .
MR
0145497
Zbl
0118.39104
People
BibTeX
@article {key0145497m,
AUTHOR = {Brown, Morton and Gluck, Herman},
TITLE = {Stable structures on manifolds},
JOURNAL = {Bull. Amer. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {69},
YEAR = {1963},
PAGES = {51--58},
NOTE = {Available at
http://dx.doi.org/10.1090/S0002-9904-1963-10855-1.
MR 26 \#3028. Zbl 0118.39104.},
ISSN = {0002-9904},
}
M. Brown and H. Gluck :
“Stable structures on manifolds, III: Applications ,”
Ann. of Math. (2)
79
(1964 ),
pp. 45–58 .
MR
0158385
People
BibTeX
@article {key0158385m,
AUTHOR = {Brown, Morton and Gluck, Herman},
TITLE = {Stable structures on manifolds, {III}:
{A}pplications},
JOURNAL = {Ann. of Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {79},
YEAR = {1964},
PAGES = {45--58},
NOTE = {Available at
http://dx.doi.org/10.2307/1970481.
MR 28 \#1608c.},
ISSN = {0003-486X},
}
M. Brown and H. Gluck :
“Stable structures on manifolds, I: Homeomorphisms of
\( S^{n} \) ,”
Ann. of Math. (2)
79
(1964 ),
pp. 1–17 .
MR
0158383
People
BibTeX
@article {key0158383m,
AUTHOR = {Brown, Morton and Gluck, Herman},
TITLE = {Stable structures on manifolds, {I}:
{H}omeomorphisms of \$S^{n}\$},
JOURNAL = {Ann. of Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {79},
YEAR = {1964},
PAGES = {1--17},
NOTE = {Available at
http://dx.doi.org/10.2307/1970481.
MR 28 \#1608a.},
ISSN = {0003-486X},
}
M. Brown and H. Gluck :
“Stable structures on manifolds, II: Stable manifolds ,”
Ann. of Math. (2)
79
(1964 ),
pp. 18–44 .
MR
0158384
People
BibTeX
@article {key0158384m,
AUTHOR = {Brown, Morton and Gluck, Herman},
TITLE = {Stable structures on manifolds, {II}:
{S}table manifolds},
JOURNAL = {Ann. of Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {79},
YEAR = {1964},
PAGES = {18--44},
NOTE = {Available at
http://dx.doi.org/10.2307/1970481.
MR 28 \#1608b.},
ISSN = {0003-486X},
}
M. Brown :
“Wild cells and spheres in higher dimensions ,”
Michigan Math. J.
14
(1967 ),
pp. 219–224 .
MR
0221481
Zbl
0147.23902
BibTeX
@article {key0221481m,
AUTHOR = {Brown, Morton},
TITLE = {Wild cells and spheres in higher dimensions},
JOURNAL = {Michigan Math. J.},
FJOURNAL = {The Michigan Mathematical Journal},
VOLUME = {14},
YEAR = {1967},
PAGES = {219--224},
NOTE = {Available at
http://dx.doi.org/10.1307/mmj/1028999719.
MR 36 \#4533. Zbl 0147.23902.},
ISSN = {0026-2285},
}
M. Brown :
“A note on Kister’s isotopy ,”
Michigan Math. J.
14
(1967 ),
pp. 95–96 .
MR
0214077
Zbl
0185.51503
BibTeX
@article {key0214077m,
AUTHOR = {Brown, M.},
TITLE = {A note on {K}ister's isotopy},
JOURNAL = {Michigan Math. J.},
FJOURNAL = {The Michigan Mathematical Journal},
VOLUME = {14},
YEAR = {1967},
PAGES = {95--96},
NOTE = {Available at
http://dx.doi.org/10.1307/mmj/1028999663.
MR 35 \#4929. Zbl 0185.51503.},
ISSN = {0026-2285},
}
M. Brown :
“Pushing graphs around ,”
pp. 19–22
in
Conference on the topology of manifolds
(Michigan State Univ., E. Lansing, MI, 1967 ).
Prindle, Weber & Schmidt (Boston ),
1968 .
MR
0234468
Zbl
0185.50601
BibTeX
@incollection {key0234468m,
AUTHOR = {Brown, Morton},
TITLE = {Pushing graphs around},
BOOKTITLE = {Conference on the topology of manifolds},
PUBLISHER = {Prindle, Weber \& Schmidt},
ADDRESS = {Boston},
YEAR = {1968},
PAGES = {19--22},
NOTE = {(Michigan State Univ., E. Lansing, MI,
1967). MR 38 \#2785. Zbl 0185.50601.},
}
M. Brown :
“A note on Cartesian products ,”
Amer. J. Math.
91
(1969 ),
pp. 32–36 .
MR
0239555
Zbl
0179.51405
BibTeX
@article {key0239555m,
AUTHOR = {Brown, Morton},
TITLE = {A note on {C}artesian products},
JOURNAL = {Amer. J. Math.},
FJOURNAL = {American Journal of Mathematics},
VOLUME = {91},
YEAR = {1969},
PAGES = {32--36},
NOTE = {Available at
http://dx.doi.org/10.2307/2373266.
MR 39 \#912. Zbl 0179.51405.},
ISSN = {0002-9327},
}
M. Brown :
“Sets of constant distance from a planar set ,”
Michigan Math. J.
19
(1972 ),
pp. 321–323 .
MR
0315714
Zbl
0244.54019
BibTeX
@article {key0315714m,
AUTHOR = {Brown, Morton},
TITLE = {Sets of constant distance from a planar
set},
JOURNAL = {Michigan Math. J.},
FJOURNAL = {The Michigan Mathematical Journal},
VOLUME = {19},
YEAR = {1972},
PAGES = {321--323},
NOTE = {Available at
http://dx.doi.org/10.1307/mmj/1029000941.
MR 47 \#4263. Zbl 0244.54019.},
ISSN = {0026-2285},
}
M. Brown :
“An application of homology theory to 4-coloring problems ,”
Nederl. Akad. Wetensch. Proc. Ser. A
75
(1972 ),
pp. 353–354 .
Also published in Indag. Math. 34 .
MR
0317312
BibTeX
@article {key0317312m,
AUTHOR = {Brown, Morton},
TITLE = {An application of homology theory to
{4}-coloring problems},
JOURNAL = {Nederl. Akad. Wetensch. Proc. Ser. A},
VOLUME = {75},
YEAR = {1972},
PAGES = {353--354},
NOTE = {Also published in \textit{Indag. Math.}
\textbf{34}. MR 47 \#5859.},
}
M. Brown and R. Connelly :
“On graphs with a constant link ,”
pp. 19–51
in
New directions in the theory of graphs
(Univ. Michigan, Ann Arbor, MI, 1971 ).
Academic Press (New York ),
1973 .
MR
0347685
Zbl
0258.05104
People
BibTeX
@incollection {key0347685m,
AUTHOR = {Brown, Morton and Connelly, Robert},
TITLE = {On graphs with a constant link},
BOOKTITLE = {New directions in the theory of graphs},
PUBLISHER = {Academic Press},
ADDRESS = {New York},
YEAR = {1973},
PAGES = {19--51},
NOTE = {(Univ. Michigan, Ann Arbor, MI, 1971).
MR 50 \#187. Zbl 0258.05104.},
}
M. Brown and R. Connelly :
“On graphs with a constant link, II ,”
Discrete Math.
11
(1975 ),
pp. 199–232 .
MR
0364016
Zbl
0304.05102
People
BibTeX
@article {key0364016m,
AUTHOR = {Brown, Morton and Connelly, Robert},
TITLE = {On graphs with a constant link, {II}},
JOURNAL = {Discrete Math.},
FJOURNAL = {Discrete Mathematics},
VOLUME = {11},
YEAR = {1975},
PAGES = {199--232},
NOTE = {Available at
http://dx.doi.org/10.1016/0012-365X(75)90037-0.
MR 51 \#271. Zbl 0304.05102.},
ISSN = {0012-365X},
}
M. Brown and W. D. Neumann :
“Proof of the Poincaré–Birkhoff fixed point theorem ,”
Mich. Math. J.
24 : 1
(1977 ),
pp. 21–31 .
MR
448339
Zbl
0402.55001
article
Abstract
People
BibTeX
The Poincaré–Birkhoff fixed point theorem (also called Poincaré’s last geometric theorem) asserts the existence of at least two fixed points for a so-called area-preserving twist homeomorphism of the annulus. It was formulated as a conjecture and proved in special cases by Poincaré [1912], shortly before his death. In [1913] George Birkhoff published a proof which, though correct for one fixed point, overlooked the passibility that this fixed point might have index 0 in deducing the existence of a second fixed point. This error was corrected in his paper [1926], in which a generalization of the theorem in question is proven, with “area-preserving” replaced by a purely topological condition and “homeomorphism” replaced by a more general situation. However, some mathematicians have claimed that this proof too is incorrect, and the last few years have seen some extensive efforts to try to find a correct proof for the second fixed point.
We present here an elementary proof for two fixed points which is a simple modification of Birkhoff’s well known original proof for one fixed point. Our modification to get the second fixed point is essentially the same modification that Birkhoff sketches in the 1926 proof of his topological version to get from one fixed point to two.
This paper is therefore in a sense an expository paper, and to make the proof as transparent as possible we shall restrict to the simplest situation — a twist homeomorphism of the annulus which is just a rotation by a fixed angle on each boundary circle. As we point out in a final section, the proof goes through almost word for word without this restriction. It also extends to more general measures than the standard Lebesgue measure on the annulus.
Since our proof is so chase to Birkhoff’s proof, which has met with some skepticism, we have felt it advisable to give somewhat more detail than would otherwise be necessary. This is also in keeping with the view of this paper as an expository one.
@article {key448339m,
AUTHOR = {Brown, M. and Neumann, W. D.},
TITLE = {Proof of the {P}oincar\'e--{B}irkhoff
fixed point theorem},
JOURNAL = {Mich. Math. J.},
FJOURNAL = {Michigan Mathematical Journal},
VOLUME = {24},
NUMBER = {1},
YEAR = {1977},
PAGES = {21--31},
DOI = {10.1307/mmj/1029001816},
URL = {http://projecteuclid.org/euclid.mmj/1029001816},
NOTE = {MR:448339. Zbl:0402.55001.},
ISSN = {0026-2285},
}
M. Brown :
“A short short proof of the Cartwright–Littlewood theorem ,”
Proc. Amer. Math. Soc.
65 : 2
(1977 ),
pp. 372 .
MR
0461491
Zbl
0369.57001
BibTeX
@article {key0461491m,
AUTHOR = {Brown, Morton},
TITLE = {A short short proof of the {C}artwright--{L}ittlewood
theorem},
JOURNAL = {Proc. Amer. Math. Soc.},
FJOURNAL = {Proceedings of the American Mathematical
Society},
VOLUME = {65},
NUMBER = {2},
YEAR = {1977},
PAGES = {372},
NOTE = {Available at
http://dx.doi.org/10.2307/2041926.
MR 57 \#1476. Zbl 0369.57001.},
ISSN = {0002-9939},
}
M. Brown and A. G. Wasserman :
“Arithmetic invariants of simplicial complexes ,”
Canad. J. Math.
32 : 6
(1980 ),
pp. 1306–1310 .
MR
604685
Zbl
0413.57013
People
BibTeX
@article {key604685m,
AUTHOR = {Brown, M. and Wasserman, A. G.},
TITLE = {Arithmetic invariants of simplicial
complexes},
JOURNAL = {Canad. J. Math.},
FJOURNAL = {Canadian Journal of Mathematics. Journal
Canadien de Math\'ematiques},
VOLUME = {32},
NUMBER = {6},
YEAR = {1980},
PAGES = {1306--1310},
NOTE = {Available at
http://dx.doi.org/10.4153/CJM-1980-100-0.
MR 82c:57011. Zbl 0413.57013.},
ISSN = {0008-414X},
CODEN = {CJMAAB},
}
B. Brechner and M. Brown :
“Mapping cylinder neighborhoods in the plane ,”
Proc. Amer. Math. Soc.
84 : 3
(1982 ),
pp. 433–436 .
MR
640248
Zbl
0478.54030
People
BibTeX
@article {key640248m,
AUTHOR = {Brechner, Beverly and Brown, Morton},
TITLE = {Mapping cylinder neighborhoods in the
plane},
JOURNAL = {Proc. Amer. Math. Soc.},
FJOURNAL = {Proceedings of the American Mathematical
Society},
VOLUME = {84},
NUMBER = {3},
YEAR = {1982},
PAGES = {433--436},
NOTE = {Available at
http://dx.doi.org/10.2307/2043577.
MR 83h:57012. Zbl 0478.54030.},
ISSN = {0002-9939},
CODEN = {PAMYAR},
}
M. Brown :
“A new proof of Brouwer’s lemma on translation arcs ,”
Houston J. Math.
10 : 1
(1984 ),
pp. 35–41 .
MR
736573
Zbl
0551.57005
BibTeX
@article {key736573m,
AUTHOR = {Brown, Morton},
TITLE = {A new proof of {B}rouwer's lemma on
translation arcs},
JOURNAL = {Houston J. Math.},
FJOURNAL = {Houston Journal of Mathematics},
VOLUME = {10},
NUMBER = {1},
YEAR = {1984},
PAGES = {35--41},
NOTE = {MR 85h:54080. Zbl 0551.57005.},
ISSN = {0362-1588},
CODEN = {HJMADZ},
}
M. Brown and J. M. Kister :
“Invariance of complementary domains of a fixed point set ,”
Proc. Amer. Math. Soc.
91 : 3
(1984 ),
pp. 503–504 .
MR
744656
Zbl
0547.57010
People
BibTeX
@article {key744656m,
AUTHOR = {Brown, M. and Kister, J. M.},
TITLE = {Invariance of complementary domains
of a fixed point set},
JOURNAL = {Proc. Amer. Math. Soc.},
FJOURNAL = {Proceedings of the American Mathematical
Society},
VOLUME = {91},
NUMBER = {3},
YEAR = {1984},
PAGES = {503--504},
NOTE = {Available at
http://dx.doi.org/10.2307/2045329.
MR 86c:57014. Zbl 0547.57010.},
ISSN = {0002-9939},
CODEN = {PAMYAR},
}
M. Brown :
“Homeomorphisms of two-dimensional manifolds ,”
Houston J. Math.
11 : 4
(1985 ),
pp. 455–469 .
MR
837985
Zbl
0605.57005
BibTeX
@article {key837985m,
AUTHOR = {Brown, M.},
TITLE = {Homeomorphisms of two-dimensional manifolds},
JOURNAL = {Houston J. Math.},
FJOURNAL = {Houston Journal of Mathematics},
VOLUME = {11},
NUMBER = {4},
YEAR = {1985},
PAGES = {455--469},
NOTE = {MR 87g:57020. Zbl 0605.57005.},
ISSN = {0362-1588},
CODEN = {HJMADZ},
}
M. Brown :
“The mathematical work of R. H. Bing ,”
pp. 1–25
in
Proceedings of the 1987 topology conference
(Birmingham, AL, 1987 ),
published as Topology Proc.
12 : 1 .
Issue edited by G. Gruenhage, D. Bennett, and L. Mohler .
Auburn University (Birmingham, AL ),
1987 .
MR
951703
Zbl
0661.01017
incollection
People
BibTeX
Read it here
@article {key951703m,
AUTHOR = {Brown, Morton},
TITLE = {The mathematical work of {R}.~{H}. {B}ing},
JOURNAL = {Topology Proc.},
FJOURNAL = {Topology Proceedings},
VOLUME = {12},
NUMBER = {1},
YEAR = {1987},
PAGES = {1--25},
URL = {http://topology.auburn.edu/tp/reprints/v12/tp12102.pdf},
NOTE = {\textit{Proceedings of the 1987 topology
conference} (Birmingham, AL, 1987).
Issue edited by G. Gruenhage,
D. Bennett, and L. Mohler.
MR:951703. Zbl:0661.01017.},
ISSN = {0146-4124},
}
M. Brown, E. E. Slaminka, and W. Transue :
“An orientation preserving fixed point free homeomorphism of
the plane which admits no closed invariant line ,”
Topology Appl.
29 : 3
(1988 ),
pp. 213–217 .
MR
953953
Zbl
0668.54024
People
BibTeX
@article {key953953m,
AUTHOR = {Brown, Morton and Slaminka, Edward E.
and Transue, William},
TITLE = {An orientation preserving fixed point
free homeomorphism of the plane which
admits no closed invariant line},
JOURNAL = {Topology Appl.},
FJOURNAL = {Topology and its Applications},
VOLUME = {29},
NUMBER = {3},
YEAR = {1988},
PAGES = {213--217},
NOTE = {Available at
http://dx.doi.org/10.1016/0166-8641(88)90020-X.
MR 89i:58076. Zbl 0668.54024.},
ISSN = {0166-8641},
CODEN = {TIAPD9},
}
M. Brown :
“Fixed points for orientation preserving homeomorphisms of the
plane which interchange two points ,”
Pacific J. Math.
143 : 1
(1990 ),
pp. 37–41 .
MR
1047399
Zbl
0728.55001
BibTeX
@article {key1047399m,
AUTHOR = {Brown, Morton},
TITLE = {Fixed points for orientation preserving
homeomorphisms of the plane which interchange
two points},
JOURNAL = {Pacific J. Math.},
FJOURNAL = {Pacific Journal of Mathematics},
VOLUME = {143},
NUMBER = {1},
YEAR = {1990},
PAGES = {37--41},
NOTE = {Available at
http://dx.doi.org/10.2140/pjm.1990.143.37.
MR 91k:54072. Zbl 0728.55001.},
ISSN = {0030-8730},
CODEN = {PJMAAI},
}
M. Brown :
“On the fixed point index of iterates of planar homeomorphisms ,”
Proc. Amer. Math. Soc.
108 : 4
(1990 ),
pp. 1109–1114 .
MR
994772
Zbl
0686.58028
BibTeX
@article {key994772m,
AUTHOR = {Brown, Morton},
TITLE = {On the fixed point index of iterates
of planar homeomorphisms},
JOURNAL = {Proc. Amer. Math. Soc.},
FJOURNAL = {Proceedings of the American Mathematical
Society},
VOLUME = {108},
NUMBER = {4},
YEAR = {1990},
PAGES = {1109--1114},
NOTE = {Available at
http://dx.doi.org/10.2307/2047977.
MR 90g:54036. Zbl 0686.58028.},
ISSN = {0002-9939},
CODEN = {PAMYAR},
}
M. Barge and M. Brown :
“Problems in dynamics on continua ,”
pp. 177–182
in
Continuum theory and dynamical systems
(Arcata, CA, 1989 ).
Contemp. Math. 117 .
Amer. Math. Soc. (Providence, RI ),
1991 .
MR
1112814
Zbl
0726.54026
People
BibTeX
@incollection {key1112814m,
AUTHOR = {Barge, Marcy and Brown, Morton},
TITLE = {Problems in dynamics on continua},
BOOKTITLE = {Continuum theory and dynamical systems},
SERIES = {Contemp. Math.},
NUMBER = {117},
PUBLISHER = {Amer. Math. Soc.},
ADDRESS = {Providence, RI},
YEAR = {1991},
PAGES = {177--182},
NOTE = {(Arcata, CA, 1989). Available at
http://dx.doi.org/10.1090/conm/117/1112814.
MR 92i:54032. Zbl 0726.54026.},
}
M. Brown :
“Fundamental regions of planar homeomorphisms ,”
pp. 49–56
in
Continuum theory and dynamical systems
(Arcata, CA, 1989 ).
Contemp. Math. 117 .
Amer. Math. Soc. (Providence, RI ),
1991 .
MR
1112802
Zbl
0732.54029
BibTeX
@incollection {key1112802m,
AUTHOR = {Brown, Morton},
TITLE = {Fundamental regions of planar homeomorphisms},
BOOKTITLE = {Continuum theory and dynamical systems},
SERIES = {Contemp. Math.},
NUMBER = {117},
PUBLISHER = {Amer. Math. Soc.},
ADDRESS = {Providence, RI},
YEAR = {1991},
PAGES = {49--56},
NOTE = {(Arcata, CA, 1989). Available at
http://dx.doi.org/10.1090/conm/117/1112802.
MR 92h:54045. Zbl 0732.54029.},
}
M. Brown :
“A periodic homeomorphism of the plane ,”
pp. 83–87
in
Continuum theory and dynamical systems .
Lecture Notes in Pure and Appl. Math. 149 .
Dekker (New York ),
1993 .
MR
1235347
Zbl
0791.58074
BibTeX
@incollection {key1235347m,
AUTHOR = {Brown, Morton},
TITLE = {A periodic homeomorphism of the plane},
BOOKTITLE = {Continuum theory and dynamical systems},
SERIES = {Lecture Notes in Pure and Appl. Math.},
NUMBER = {149},
PUBLISHER = {Dekker},
ADDRESS = {New York},
YEAR = {1993},
PAGES = {83--87},
NOTE = {MR 94d:54088. Zbl 0791.58074.},
}
K. Boucher, M. Brown, and E. E. Slaminka :
“A Nielsen-type theorem for area-preserving homeomorphisms of
the two disc ,”
pp. 43–50
in
Continuum theory and dynamical systems .
Lecture Notes in Pure and Appl. Math. 149 .
Dekker (New York ),
1993 .
MR
1235344
Zbl
0807.58027
People
BibTeX
@incollection {key1235344m,
AUTHOR = {Boucher, Kenneth and Brown, Morton and
Slaminka, Edward E.},
TITLE = {A {N}ielsen-type theorem for area-preserving
homeomorphisms of the two disc},
BOOKTITLE = {Continuum theory and dynamical systems},
SERIES = {Lecture Notes in Pure and Appl. Math.},
NUMBER = {149},
PUBLISHER = {Dekker},
ADDRESS = {New York},
YEAR = {1993},
PAGES = {43--50},
NOTE = {MR 94e:55001. Zbl 0807.58027.},
}