TY - JOUR

T1 - Multidimensional diffeomorphisms with stable periodic points

AU - Vasil'Eva, E. V.

PY - 2011/12/1

Y1 - 2011/12/1

N2 - A self-diffeomorphism of (n+m)-space with a fixed hyperbolic point at the origin was considered. The existence of a nontransversal homoclinic point is assumed. It has been proved that when the stable and unstable manifolds are tangent in a certain way, a neighborhood of the homoclinic point may contain stable periodic points, but at least one of the characteristic exponents for such points tends to zero with increasing the period. f is supposed to be a self diffeomorphism of (n + m)-space. W s(0), W u(0) denote the stable and unstable manifolds of the point 0. It is proved that the neighborhood U may contain a countable set of stable periodic points, but at least one of the characteristic exponents for such points tends to zero with increasing the period.

AB - A self-diffeomorphism of (n+m)-space with a fixed hyperbolic point at the origin was considered. The existence of a nontransversal homoclinic point is assumed. It has been proved that when the stable and unstable manifolds are tangent in a certain way, a neighborhood of the homoclinic point may contain stable periodic points, but at least one of the characteristic exponents for such points tends to zero with increasing the period. f is supposed to be a self diffeomorphism of (n + m)-space. W s(0), W u(0) denote the stable and unstable manifolds of the point 0. It is proved that the neighborhood U may contain a countable set of stable periodic points, but at least one of the characteristic exponents for such points tends to zero with increasing the period.

UR - http://www.scopus.com/inward/record.url?scp=84856950251&partnerID=8YFLogxK

U2 - 10.1134/S1064562411070210

DO - 10.1134/S1064562411070210

M3 - Article

AN - SCOPUS:84856950251

VL - 84

SP - 808

EP - 810

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - 3

ER -