TY - JOUR

T1 - One-Parameter Set of Diffeormorphisms of the Plane with Stable Periodic Points

AU - Vasil’eva, E. V.

N1 - 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

PY - 2022/2

Y1 - 2022/2

N2 - 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.

AB - 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.

KW - characteristic exponents

KW - nontransverse homoclinic points

KW - stable periodic points

KW - two-dimensional diffeomorphisms

UR - http://www.scopus.com/inward/record.url?scp=85127371784&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/086b21b9-2eda-31a2-9955-44e37d9eb9d2/

U2 - 10.1134/s1995080222020172

DO - 10.1134/s1995080222020172

M3 - Article

AN - SCOPUS:85127371784

VL - 42

SP - 3543

EP - 3549

JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

SN - 1995-0802

IS - 14

ER -