V. I. Arnol’d, A. M. Vershik, O. Ya. Viro, A. N. Kolmogorov, S. P. Novikov, Ya. G. Sinaj, and D. B. Fuks :
“Vladimir Abramovich Rokhlin (obituary) ,”
Usp. Mat. Nauk
41 : 3(249)
(1986 ),
pp. 159–163 .
An English translation was published in Russ. Math. Surv. 41 :3(1986) .
MR
854242
Zbl
0604.01010
article
People
BibTeX
@article {key854242m,
AUTHOR = {Arnol\cprime d, V. I. and Vershik, A.
M. and Viro, O. Ya. and Kolmogorov,
A. N. and Novikov, S. P. and Sinaj,
Ya. G. and Fuks, D. B.},
TITLE = {Vladimir {A}bramovich {R}okhlin (obituary)},
JOURNAL = {Usp. Mat. Nauk},
FJOURNAL = {Uspekhi Matematicheskikh Nauk [N.S.]},
VOLUME = {41},
NUMBER = {3(249)},
YEAR = {1986},
PAGES = {159--163},
URL = {http://mi.mathnet.ru/eng/umn2084},
NOTE = {An English translation was published
in \textit{Russ. Math. Surv.} \textbf{41}:3(1986).
MR:854242. Zbl:0604.01010.},
ISSN = {0042-1316},
}
V. I. Arnol’d, A. M. Vershik, O. Ya. Viro, A. N. Kolmogorov, S. P. Novikov, Ya. G. Sinaj, and D. B. Fuks :
“Vladimir Abramovich Rokhlin (obituary) ,”
Russ. Math. Surv.
41 : 3
(June 1986 ),
pp. 189–195 .
English translation of Russian original published in Usp. Mat. Nauk 41 :3(249) (1986) .
Zbl
0608.01032
article
People
BibTeX
@article {key0608.01032z,
AUTHOR = {Arnol\cprime d, V. I. and Vershik, A.
M. and Viro, O. Ya. and Kolmogorov,
A. N. and Novikov, S. P. and Sinaj,
Ya. G. and Fuks, D. B.},
TITLE = {Vladimir {A}bramovich {R}okhlin (obituary)},
JOURNAL = {Russ. Math. Surv.},
FJOURNAL = {Russian Mathematical Surveys},
VOLUME = {41},
NUMBER = {3},
MONTH = {June},
YEAR = {1986},
PAGES = {189--195},
DOI = {10.1070/RM1986v041n03ABEH003331},
NOTE = {English translation of Russian original
published in \textit{Usp. Mat. Nauk}
\textbf{41}:3(249) (1986). Zbl:0608.01032.},
ISSN = {0036-0279},
}
A. Fialowski and D. Fuchs :
“Singular deformations of Lie algebras: Example: Deformations of the Lie algebra \( L_1 \) ,”
pp. 77–92
in
Topics in singularity theory: V. I. Arnold’s 60th anniversary collection .
Edited by A. Khovanskiĭ, A. Varchenko, and V. Vassiliev .
AMS Translations. Series 2 180 .
American Mathematical Society (Providence, RI ),
1997 .
MR
1767113
Zbl
0883.17023
ArXiv
q-alg/9706027
incollection
Abstract
People
BibTeX
In this article we consider singular deformations of Lie algebras, i.e., nontrivial deformations with zero infinitesimal parts. We show that deformations with essential singularities unavoidably arise in the classification of deformations of some of the simplest infinite-dimensional Lie algebras.
@incollection {key1767113m,
AUTHOR = {Fialowski, Alice and Fuchs, Dmitry},
TITLE = {Singular deformations of {L}ie algebras:
{E}xample: {D}eformations of the {L}ie
algebra \$L_1\$},
BOOKTITLE = {Topics in singularity theory: {V}.~{I}.
{A}rnold's 60th anniversary collection},
EDITOR = {Khovanski\u{\i}, A. and Varchenko, A.
and Vassiliev, V.},
SERIES = {AMS Translations. Series 2},
NUMBER = {180},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {1997},
PAGES = {77--92},
DOI = {10.1090/trans2/180/05},
NOTE = {ArXiv:q-alg/9706027. MR:1767113. Zbl:0883.17023.},
ISSN = {0065-9290},
ISBN = {9780821808078},
}
D. Davis, D. Fuchs, and S. Tabachnikov :
“Periodic trajectories in the regular pentagon ,”
Mosc. Math. J.
11 : 3
(July–September 2011 ),
pp. 439–461 .
To the memory of V. I. Arnold.
MR
2894424
Zbl
1276.37033
ArXiv
1102.1005
article
Abstract
People
BibTeX
We consider periodic billiard trajectories in a regular pentagon. It is known that the trajectory is periodic if and only if the tangent of the angle formed by the trajectory and the side of the pentagon belongs to \( (\sin 36^{\circ})\mathbb{Q}[\sqrt{5}] \) . Moreover, for every such direction, the lengths of the trajectories, both geometric and combinatorial, take precisely two values. In this paper, we provide a full computation of these lengths as well as a full description of the corresponding symbolic orbits. We also formulate results and conjectures regarding the billiards in other regular polygons.
@article {key2894424m,
AUTHOR = {Davis, Diana and Fuchs, Dmitry and Tabachnikov,
Serge},
TITLE = {Periodic trajectories in the regular
pentagon},
JOURNAL = {Mosc. Math. J.},
FJOURNAL = {Moscow Mathematical Journal},
VOLUME = {11},
NUMBER = {3},
MONTH = {July--September},
YEAR = {2011},
PAGES = {439--461},
URL = {http://www.mathjournals.org/mmj/vol11-3-2011/davis-etal.pdf},
NOTE = {To the memory of V.~I. Arnold. ArXiv:1102.1005.
MR:2894424. Zbl:1276.37033.},
ISSN = {1609-3321},
}
D. Fuchs, Y. Ilyashenko, B. Khesin, V. Vassiliev, and H. Hofer :
“Memories of Vladimir Arnold ,”
Notices Am. Math. Soc.
59 : 4
(April 2012 ),
pp. 482–502 .
Coordinating editors were Boris Khesin and Serge Tabchnikov.
MR
2951953
Zbl
1284.37002
article
Abstract
People
BibTeX
Vladimir Arnold, an eminent mathematician of our time, passed away on June 3, 2010, nine days before his seventy-third birthday. This article, along with one in the previous issue of the Notices , touches on his outstanding personality and his great contribution to mathematics.
@article {key2951953m,
AUTHOR = {Fuchs, Dmitry and Ilyashenko, Yulij
and Khesin, Boris and Vassiliev, Victor
and Hofer, Helmut},
TITLE = {Memories of {V}ladimir {A}rnold},
JOURNAL = {Notices Am. Math. Soc.},
FJOURNAL = {Notices of the American Mathematical
Society},
VOLUME = {59},
NUMBER = {4},
MONTH = {April},
YEAR = {2012},
PAGES = {482--502},
URL = {https://www.ams.org/journals/notices/201204/rtx120400482p.pdf},
NOTE = {Coordinating editors were Boris Khesin
and Serge Tabchnikov. MR:2951953. Zbl:1284.37002.},
ISSN = {0002-9920},
}
D. Fuchs :
“Dima Arnold in my life ,”
pp. 133–140
in
Arnold: Swimming against the tide .
Edited by B. A. Khesin and S. L. Tabachnikov .
American Mathematical Society (Providence, RI ),
2014 .
incollection
People
BibTeX
@incollection {key34494588,
AUTHOR = {Fuchs, Dmitry},
TITLE = {Dima {A}rnold in my life},
BOOKTITLE = {Arnold: {S}wimming against the tide},
EDITOR = {Khesin, Boris A. and Tabachnikov, Serge
L.},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {2014},
PAGES = {133--140},
ISBN = {9781470416997},
}