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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2007, Volume 3, Number 4, Pages 423–443
(Mi nd149)
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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.
Citation:
S. V. Gonchenko, A. S. Gonchenko, “Towards a classification of linear and nonlinear smale horseshoes”, Nelin. Dinam., 3:4 (2007), 423–443
Linking options:
https://www.mathnet.ru/eng/nd149 https://www.mathnet.ru/eng/nd/v3/i4/p423
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Abstract page: | 333 | Full-text PDF : | 136 | First page: | 1 |
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