M. L. Cartwright and J. E. Littlewood :
“On non-linear differential equations of the second order, I ,”
J. London Math. Soc.
20 : 3
(1945 ),
pp. 180–189 .
Part II published in Ann. Math. 48 :2 (1947) .
MR
0016789
Zbl
0061.18903
article
People
BibTeX
@article {key0016789m,
AUTHOR = {Cartwright, M. L. and Littlewood, J.
E.},
TITLE = {On non-linear differential equations
of the second order, {I}},
JOURNAL = {J. London Math. Soc.},
FJOURNAL = {Journal of the London Mathematical Society.
Second Series},
VOLUME = {20},
NUMBER = {3},
YEAR = {1945},
PAGES = {180--189},
DOI = {10.1112/jlms/s1-20.3.180},
NOTE = {Part II published in \textit{Ann. Math.}
\textbf{48}:2 (1947). MR:0016789. Zbl:0061.18903.},
ISSN = {0024-6107},
}
M. L. Cartwright and J. E. Littlewood :
“On non-linear differential equations of the second order, II ,”
Ann. Math. (2)
48 : 2
(April 1947 ),
pp. 472–494 .
Part I published in J. London Math. Soc. 20 :3 (1945) . Addendum published in Ann. Math. 48 :2 (1947) , errata pubished in Ann. Math. 50 :2 (1949) .
MR
0021190
article
Abstract
People
BibTeX
The present paper is mainly a study of the equation
\[ \ddot y+kf(y) \dot y+g(y,k)=p(t)=p_1(t)+kp_2(t), \]
for \( k > 0 \) and \( f(y)\geqq 1 \) , in real variables in the case when the damping factor \( kf(y) \) is always positive.
@article {key0021190m,
AUTHOR = {Cartwright, M. L. and Littlewood, J.
E.},
TITLE = {On non-linear differential equations
of the second order, {II}},
JOURNAL = {Ann. Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {48},
NUMBER = {2},
MONTH = {April},
YEAR = {1947},
PAGES = {472--494},
DOI = {10.2307/1969181},
NOTE = {Part I published in \textit{J. London
Math. Soc.} \textbf{20}:3 (1945). Addendum
published in \textit{Ann. Math.} \textbf{48}:2
(1947), errata pubished in \textit{Ann.
Math.} \textbf{50}:2 (1949). MR:0021190.},
ISSN = {0003-486X},
}
M. L. Cartwright and J. E. Littlewood :
“Errata: ‘On non-linear differential equations of the second order, II’ ,”
Ann. Math. (2)
49 : 4
(October 1948 ),
pp. 1010 .
Errata for article published in Ann. Math. 48 :2 (1947) .
MR
0026200
article
People
BibTeX
@article {key0026200m,
AUTHOR = {Cartwright, M. L. and Littlewood, J.
E.},
TITLE = {Errata: ``{O}n non-linear differential
equations of the second order, {II}''},
JOURNAL = {Ann. Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {49},
NUMBER = {4},
MONTH = {October},
YEAR = {1948},
PAGES = {1010},
DOI = {10.2307/1969411},
NOTE = {Errata for article published in \textit{Ann.
Math.} \textbf{48}:2 (1947). MR:0026200.},
ISSN = {0003-486X},
}
M. L. Cartwright and J. E. Littlewood :
“Addendum to ‘On non-linear differential equations of the second order, II’ ,”
Ann. Math. (2)
50 : 2
(April 1949 ),
pp. 504–505 .
Addendum to article published in Ann. Math. 48 :2 (1947) .
MR
0030078
Zbl
0038.25001
article
People
BibTeX
@article {key0030078m,
AUTHOR = {Cartwright, M. L. and Littlewood, J.
E.},
TITLE = {Addendum to `{O}n non-linear differential
equations of the second order, {II}'},
JOURNAL = {Ann. Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {50},
NUMBER = {2},
MONTH = {April},
YEAR = {1949},
PAGES = {504--505},
DOI = {10.2307/1969465},
NOTE = {Addendum to article published in \textit{Ann.
Math.} \textbf{48}:2 (1947). MR:0030078.
Zbl:0038.25001.},
ISSN = {0003-486X},
}
M. L. Cartwright and J. E. Littlewood :
“Some fixed point theorems ,”
Ann. Math. (2)
54 : 1
(July 1951 ),
pp. 1–37 .
With an appendix by H. D. Ursell.
MR
0042690
Zbl
0058.38604, 0054.07101
article
Abstract
People
BibTeX
We propose to discuss certain fixed point problems in the plane which are connected with the theory of certain differential equations suggested by physical problems mainly equations of the form
\[ \ddot{\xi} + f(\xi)\dot{\xi} + g(\xi) = p(t) ,\]
where \( f \) , \( p \) are continuous, \( g \) satisfies a Lipschitz condition, \( p(t) \) has period 1, and \( g(\xi)/\xi \geq 1 \) for large \( \xi \) at any rate. Our choice of hypotheses and the main lines of our investigations have been dominated by what is significant in the theory of differential equations, but our results are concerned solely with sets of points and transformations of sets of points.
@article {key0042690m,
AUTHOR = {Cartwright, M. L. and Littlewood, J.
E.},
TITLE = {Some fixed point theorems},
JOURNAL = {Ann. Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {54},
NUMBER = {1},
MONTH = {July},
YEAR = {1951},
PAGES = {1--37},
DOI = {10.2307/1969308},
NOTE = {With an appendix by H.~D. Ursell. MR:0042690.
Zbl:0058.38604, 0054.07101.},
ISSN = {0003-486X},
}
J. E. Littlewood and M. L. Cartwright :
“Some topological problems connected with forced oscillations ,”
pp. 429–430
in
Proceedings of the International Congress of Mathematicians
(Cambridge, MA, 30 August–6 September 1950 ),
vol. 1 .
American Mathematical Society (Providence, RI ),
1952 .
incollection
People
BibTeX
@incollection {key46850629,
AUTHOR = {Littlewood, J. E. and Cartwright, Mary
L.},
TITLE = {Some topological problems connected
with forced oscillations},
BOOKTITLE = {Proceedings of the {I}nternational {C}ongress
of {M}athematicians},
VOLUME = {1},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {1952},
PAGES = {429--430},
URL = {http://www.mathunion.org/ICM/ICM1950.1/ICM1950.1.ocr.pdf},
NOTE = {(Cambridge, MA, 30 August--6 September
1950).},
}
M. L. Cartwright :
“Equicontinuous mappings of plane minimal sets ,”
Proc. London Math. Soc. (3)
14A : 1
(1965 ),
pp. 51–54 .
Dedicated to J. E. Littlewood on his 80th birthday.
MR
0177395
Zbl
0129.38705
article
Abstract
People
BibTeX
Let \( f \) be a homeomorphism of the plane which maps a compact plane set \( M \) on to itself in such a way that the iterates \( f^n \) , \( n = 0 \) , \( \pm 1 \) , \( \pm 2,\dots \) , form an equicontinuous family on \( M \) . Suppose further that \( M \) is a minimal set, that is to say, closed and invariant and irreducible with respect to these properties. Then \( M \) is the orbit-closure of every point \( p \) of \( M \) . It is well known that if \( M \) is zero-dimensional then \( f \) is isochronous (regularly almost periodic). Further, Hemmingsen [1954] has shown that if \( M \) is connected then \( M \) is a simple closed curve and \( f \) is an irrational rotation. It follows that if \( M \) has \( n \) components then each component is a simple closed curve and \( f^n \) is an irrational rotation on each. The object of this note is to show that these are the only possible types of minimal set in the plane on which the mapping has equicontinuous iterates. That is to say there are no minimal sets with an infinity of components other than zero-dimensional sets for which the mapping has equicontinuous iterates .
@article {key0177395m,
AUTHOR = {Cartwright, M. L.},
TITLE = {Equicontinuous mappings of plane minimal
sets},
JOURNAL = {Proc. London Math. Soc. (3)},
FJOURNAL = {Proceedings of the London Mathematical
Society. Third Series},
VOLUME = {14A},
NUMBER = {1},
YEAR = {1965},
PAGES = {51--54},
DOI = {10.1112/plms/s3-14A.1.51},
NOTE = {Dedicated to J.~E. Littlewood on his
80th birthday. MR:0177395. Zbl:0129.38705.},
ISSN = {0024-6115},
}
M. Cartwright :
“Some exciting mathematical episodes involving J. E. L. ,”
pp. 201–202
in
Papers presented at the Symposium on Excitement in Mathematics
(Cambridge, 1975 ),
published as Bull. Inst. Math. Appl.
12 : 7
(1976 ).
MR
0532531
incollection
People
BibTeX
@article {key0532531m,
AUTHOR = {Cartwright, Mary},
TITLE = {Some exciting mathematical episodes
involving {J}.~{E}.~{L}.},
JOURNAL = {Bull. Inst. Math. Appl.},
FJOURNAL = {Bulletin of the Institute of Mathematics
and its Applications},
VOLUME = {12},
NUMBER = {7},
YEAR = {1976},
PAGES = {201--202},
NOTE = {\textit{Papers presented at the {S}ymposium
on {E}xcitement in {M}athematics} (Cambridge,
1975). MR:0532531.},
ISSN = {0905-5628},
}
M. L. Cartwright :
“J. E. Littlewood ,”
Nature
271 : 5641
(1978 ),
pp. 193 .
article
People
BibTeX
@article {key98865195,
AUTHOR = {Cartwright, Mary L.},
TITLE = {J.~{E}. {L}ittlewood},
JOURNAL = {Nature},
VOLUME = {271},
NUMBER = {5641},
YEAR = {1978},
PAGES = {193},
DOI = {10.1038/271193a0},
}
M. Cartwright :
“John Edensor Littlewood ,”
Bull. Inst. Math. Appl.
14 : 4
(1978 ),
pp. 87–90 .
MR
0497782
article
People
BibTeX
@article {key0497782m,
AUTHOR = {Cartwright, Mary},
TITLE = {John {E}densor {L}ittlewood},
JOURNAL = {Bull. Inst. Math. Appl.},
FJOURNAL = {Bulletin of the Institute of Mathematics
and its Applications},
VOLUME = {14},
NUMBER = {4},
YEAR = {1978},
PAGES = {87--90},
NOTE = {MR:0497782.},
ISSN = {0905-5628},
}
M. L. Cartwright :
“Some Hardy–Littlewood manuscripts ,”
Bull. London Math. Soc.
13 : 4
(1981 ),
pp. 273–300 .
MR
620040
Zbl
0464.01004
article
Abstract
People
BibTeX
This is an account of work on certain MSS of Hardy and Littlewood in the Wren Library at Trinity College, Cambridge, and in the University Library, Cambridge.
@article {key620040m,
AUTHOR = {Cartwright, M. L.},
TITLE = {Some {H}ardy--{L}ittlewood manuscripts},
JOURNAL = {Bull. London Math. Soc.},
FJOURNAL = {The Bulletin of the London Mathematical
Society},
VOLUME = {13},
NUMBER = {4},
YEAR = {1981},
PAGES = {273--300},
DOI = {10.1112/blms/13.4.273},
NOTE = {MR:620040. Zbl:0464.01004.},
ISSN = {0024-6093},
CODEN = {LMSBBT},
}
M. L. Cartwright :
“Manuscripts of Hardy, Littlewood, Marcel Riesz and Titchmarsh ,”
Bull. London Math. Soc.
14 : 6
(1982 ),
pp. 472–532 .
MR
679927
Zbl
0501.01009
article
Abstract
People
BibTeX
In an earlier article, ‘Some Hardy–Littlewood manuscripts’, this Bulletin , 13 (1981), 273–300, I gave a general account of manuscripts of Hardy and Littlewood in the Library of Trinity College, Cambridge, and the University Library, Cambridge. In this one I consider certain of those manuscripts relating to the earlier stages of ‘the body of work’ referred to by Hardy and Littlewood in ‘Theorems concerning mean values of analytic or harmonic functions’ [1941] as having occupied them ‘at intervals since 1924’.
@article {key679927m,
AUTHOR = {Cartwright, M. L.},
TITLE = {Manuscripts of {H}ardy, {L}ittlewood,
{M}arcel {R}iesz and {T}itchmarsh},
JOURNAL = {Bull. London Math. Soc.},
FJOURNAL = {The Bulletin of the London Mathematical
Society},
VOLUME = {14},
NUMBER = {6},
YEAR = {1982},
PAGES = {472--532},
DOI = {10.1112/blms/14.6.472},
NOTE = {MR:679927. Zbl:0501.01009.},
ISSN = {0024-6093},
CODEN = {LMSBBT},
}
M. L. Cartwright :
“Later Hardy and Littlewood manuscripts ,”
Bull. London Math. Soc.
17 : 4
(1985 ),
pp. 318–390 .
MR
806635
Zbl
0579.01009
article
Abstract
People
BibTeX
This is a continuation of my article ‘Manuscripts of Hardy, Littlewood, Marcel Riesz and Titchmarsh’, this Bulletin 14 (1982) 472–532, about manuscripts relating to the earlier stages of the ‘body of work’ referred to in ‘Theorems concerning mean values of analytic or harmonic functions’ [Hardy 1941].
@article {key806635m,
AUTHOR = {Cartwright, M. L.},
TITLE = {Later {H}ardy and {L}ittlewood manuscripts},
JOURNAL = {Bull. London Math. Soc.},
FJOURNAL = {The Bulletin of the London Mathematical
Society},
VOLUME = {17},
NUMBER = {4},
YEAR = {1985},
PAGES = {318--390},
DOI = {10.1112/blms/17.4.318},
NOTE = {MR:806635. Zbl:0579.01009.},
ISSN = {0024-6093},
CODEN = {LMSBBT},
}
S. L. McMurran and J. J. Tattersall :
“The mathematical collaboration of M. L. Cartwright and J. E. Littlewood ,”
Amer. Math. Mon.
103 : 10
(1996 ),
pp. 833–845 .
MR
1427114
Zbl
0887.01017
article
People
BibTeX
@article {key1427114m,
AUTHOR = {McMurran, Shawnee L. and Tattersall,
James J.},
TITLE = {The mathematical collaboration of {M}.~{L}.
{C}artwright and {J}.~{E}. {L}ittlewood},
JOURNAL = {Amer. Math. Mon.},
FJOURNAL = {The American Mathematical Monthly},
VOLUME = {103},
NUMBER = {10},
YEAR = {1996},
PAGES = {833--845},
DOI = {10.2307/2974608},
NOTE = {MR:1427114. Zbl:0887.01017.},
ISSN = {0002-9890},
CODEN = {AMMYAE},
}