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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.
Original language | English |
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Pages (from-to) | 3543-3549 |
Number of pages | 7 |
Journal | Lobachevskii Journal of Mathematics |
Volume | 42 |
Issue number | 14 |
DOIs | |
State | Published - Feb 2022 |
ID: 95511604