Geodesic
Towards a classification of linear and nonlinear smale horseshoes
Russian journal of nonlinear dynamics, Tome 3 (2007) no. 4, pp. 423-443.

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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. 
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     title = {Towards a classification of linear and nonlinear smale horseshoes},
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S. V. Gonchenko; A. S. Gonchenko. Towards a classification of linear and nonlinear smale horseshoes. Russian journal of nonlinear dynamics, Tome 3 (2007) no. 4, pp. 423-443. http://geodesic.mathdoc.fr/item/ND_2007_3_4_a4/