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Nelin. Dinam., 2007, Volume 3, Number 4, Pages 423–443 (Mi nd149)  

This article is cited in 3 scientific papers (total in 3 papers)

Towards a classification of linear and nonlinear smale horseshoes

S. V. Gonchenkoa, A. S. Gonchenkob

a Research Institute for Applied Mathematics and Cybernetics
b State University of Nizhni Novgorod

Abstract: We consider the problem of classification of Smale horseshoes from point of view of the local topological conjugacy of two-dimensionalmaps which generate the horseshoes.We show that there are 10 different types of linear horseshoes. As it was established in the recent paper [4], there are infinitelymany different types of nonlinear horseshoes. All of them belong to the class of the so-called half-orientable horseshoes and can be realized for endomorphisms (not one-to-one maps) of disk or for diffeomorphisms of non-orientable two-dimensional manifolds. We give also a short review of related results from [4].

Keywords: Smale horseshoe, local topological conjugacy, hyperbolic set, standard and generalized Hénon maps.

Full text: PDF file (897 kB)
UDC: 517.9
MSC: 37Dxx, 37D20

Citation: S. V. Gonchenko, A. S. Gonchenko, “Towards a classification of linear and nonlinear smale horseshoes”, Nelin. Dinam., 3:4 (2007), 423–443

Citation in format AMSBIB
\Bibitem{GonGon07}
\by S.~V.~Gonchenko, A.~S.~Gonchenko
\paper Towards a classification of linear and nonlinear smale horseshoes
\jour Nelin. Dinam.
\yr 2007
\vol 3
\issue 4
\pages 423--443
\mathnet{http://mi.mathnet.ru/nd149}


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    This publication is cited in the following articles:
    1. Kuznetsov A.P., Savin A.V., Sedova Yu.V., “Bifurkatsiya Bogdanova-Takensa: ot nepreryvnoi k diskretnoi modeli”, Izv. vuzov. Prikladnaya nelineinaya dinamika, 17:6 (2009), 139–158  elib
    2. S. V. Gonchenko, A. S. Gonchenko, M. I. Malkin, “O klassifikatsii klassicheskikh i poluorientiruemykh podkov v terminakh granichnykh tochek”, Nelineinaya dinam., 6:3 (2010), 549–566  mathnet  elib
    3. A. P. Kuznetsov, S. P. Kuznetsov, M. V. Pozdnyakov, Yu. V. Sedova, “Universalnoe dvumernoe otobrazhenie i ego radiofizicheskaya realizatsiya”, Nelineinaya dinam., 8:3 (2012), 461–471  mathnet
  • Нелинейная динамика
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