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One-Parameter Set of Diffeormorphisms of the Plane with Stable Periodic Points

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Abstract

In this paper we consider two-dimensional diffeomorphisms with hyperbolic fixed points and nontransverse homoclinic points. It is assumed that the tangency of a stable and unstable manifolds is not a tangency of finite order. It is shown that there exists a continuous one-parameter set of two-dimensional diffeomorphisms such that each diffeomorphism in a neighborhood of a homoclinic point has an infinite set of stable periodic points whose characteristic exponents are separated from zero.

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Funding

This study was supported by the Russian Foundation for Basic Research (grant no. 19-01-00388).

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Authors and Affiliations

  1. St. Petersburg State University, 199034, St. Petersburg, Russia

    E. V. Vasil’eva

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  1. E. V. Vasil’eva
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Correspondence to E. V. Vasil’eva.

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(Submitted by S. Yu. Pilyugin)

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Vasil’eva, E.V. One-Parameter Set of Diffeormorphisms of the Plane with Stable Periodic Points. Lobachevskii J Math 42, 3543–3549 (2021). https://doi.org/10.1134/S1995080222020172

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  • DOI: https://doi.org/10.1134/S1995080222020172

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