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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2007, Volume 256, Pages 54–69 (Mi tm455)  
This article is cited in 15 scientific papers (total in 15 papers)

Bifurcations of Morse–Smale Diffeomorphisms with Wildly Embedded Separatrices

C. Bonattia, V. Z. Grinesb, V. S. Medvedevc, O. V. Pochinkac

a Université de Bourgogne
b Nizhnii Novgorod State Agricultural Academy
c N. I. Lobachevski State University of Nizhni Novgorod
Full-text PDF (320 kB) Citations (15)
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Abstract: We study bifurcations of Morse–Smale diffeomorphisms under a change of the embedding of the separatrices of saddle periodic points in the ambient 3-manifold. The results obtained are based on the following statement proved in this paper: for the 3-sphere, the space of diffeomorphisms of North Pole–South Pole type endowed with the $C^1$ topology is connected. This statement is shown to be false in dimension 6.
Received in July 2006
English version:
Proceedings of the Steklov Institute of Mathematics, 2007, Volume 256, Pages 47–61
DOI: https://doi.org/10.1134/S0081543807010038
Bibliographic databases:
UDC: 513.83
Language: Russian
Citation: C. Bonatti, V. Z. Grines, V. S. Medvedev, O. V. Pochinka, “Bifurcations of Morse–Smale Diffeomorphisms with Wildly Embedded Separatrices”, Dynamical systems and optimization, Collected papers. Dedicated to the 70th birthday of academician Dmitrii Viktorovich Anosov, Trudy Mat. Inst. Steklova, 256, Nauka, MAIK «Nauka/Inteperiodika», M., 2007, 54–69; Proc. Steklov Inst. Math., 256 (2007), 47–61
Citation in format AMSBIB
\Bibitem{BonGriMed07}
\by C.~Bonatti, V.~Z.~Grines, V.~S.~Medvedev, O.~V.~Pochinka
\paper Bifurcations of Morse--Smale Diffeomorphisms with Wildly Embedded Separatrices
\inbook Dynamical systems and optimization
\bookinfo Collected papers. Dedicated to the 70th birthday of academician Dmitrii Viktorovich Anosov
\serial Trudy Mat. Inst. Steklova
\yr 2007
\vol 256
\pages 54--69
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm455}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2336893}
\zmath{https://zbmath.org/?q=an:1153.37340}
\elib{https://elibrary.ru/item.asp?id=9482608}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2007
\vol 256
\pages 47--61
\crossref{https://doi.org/10.1134/S0081543807010038}
\elib{https://elibrary.ru/item.asp?id=13543239}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34248351535}
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    • This publication is cited in the following 15 articles:
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