TY - JOUR

T1 - To the question of stability of periodic points of three-dimensional diffeomorphisms

AU - Vasilieva, E. V.

N1 - Vestnik St. Petersburg University. Mathematics. 2017. Volume 50, issue 2, pp. 111-116

PY - 2017/4/1

Y1 - 2017/4/1

N2 - Self-diffeomorphisms of three-dimensional space with a hyperbolic fixed point at the origin and a nontransversal point homoclinic to it are considered. It is assumed that the Jacobian matrix of the initial diffeomorphism has complex eigenvalues at the origin. It is shown that, under certain conditions imposed mainly on the character of tangency of the stable and unstable manifolds, a neighborhood of the nontransversal homoclinic point contains an infinite set of stable periodic points whose characteristic exponents are bounded away from zero.

AB - Self-diffeomorphisms of three-dimensional space with a hyperbolic fixed point at the origin and a nontransversal point homoclinic to it are considered. It is assumed that the Jacobian matrix of the initial diffeomorphism has complex eigenvalues at the origin. It is shown that, under certain conditions imposed mainly on the character of tangency of the stable and unstable manifolds, a neighborhood of the nontransversal homoclinic point contains an infinite set of stable periodic points whose characteristic exponents are bounded away from zero.

KW - hyperbolic point

KW - nontransversal homoclinic point

KW - stability

KW - three-dimensional diffeomorphism

KW - nontransversal homoclinic points

KW - stable periodic solutions

KW - periodic systems

UR - http://www.scopus.com/inward/record.url?scp=85022030164&partnerID=8YFLogxK

U2 - 10.3103/S1063454117020133

DO - 10.3103/S1063454117020133

M3 - Article

AN - SCOPUS:85022030164

VL - 50

SP - 111

EP - 116

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 2

ER -