Abstract
We consider self-diffeomorphisms of the plane of the class C r (1 ≤ r < ∞) with a fixed hyperbolic point and a nontransversal point homoclinic to it. We present a method for constructing a set of diffeomorphisms for which the neighborhood of a homoclinic point contains countably many stable periodic points with characteristic exponents bounded away from zero.
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Vasil’eva, E.V., Diffeomorphisms of the Plane with Stable Periodic Points, Differ. Uravn., 2012, vol. 48, no. 3, pp. 307–315.
Vasil’eva, E.V., Stable Periodic Points of Two-Dimensional C 1-Diffeomorphisms, Vestnik St. Petersburg Univ. Mat., 2007, no. 2, pp. 20–26.
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Original Russian Text © E.V. Vasil’eva, 2012, published in Differentsial’nye Uravneniya, 2012, Vol. 48, No. 10, pp. 1355–1360.
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Vasil’eva, E.V. Smooth diffeomorphisms of the plane with stable periodic points in a neighborhood of a homoclinic point. Diff Equat 48, 1335–1340 (2012). https://doi.org/10.1134/S0012266112100023
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DOI: https://doi.org/10.1134/S0012266112100023