TY - JOUR

T1 - Multidimentional Diffeomorphisms with Stable Periodic Points

AU - Vasil'eva, E.V.

N1 - E.V.Vasil'eva. Multidimentional Diffeomorphisms with Stable Periodic Point, Vestnik St. Petersburg University. Mathematics, 2019. Vol. 52, issue 4, pp.380-387.

PY - 2019

Y1 - 2019

N2 - The conditions are obtained for the existence of an infinite set of stable periodicpoints whose characteristic exponents are separated from zero in the neighborhood of the non-transversal homoclinic point. The conditions are imposed, first of all, on the method of tangency of a stable manifold with an unstable one; however, the proof of the theorem essentially uses the properties of the eigenvalues of the Jacobi matrix at a hyperbolic point.

AB - The conditions are obtained for the existence of an infinite set of stable periodicpoints whose characteristic exponents are separated from zero in the neighborhood of the non-transversal homoclinic point. The conditions are imposed, first of all, on the method of tangency of a stable manifold with an unstable one; however, the proof of the theorem essentially uses the properties of the eigenvalues of the Jacobi matrix at a hyperbolic point.

KW - multidimensional diffeomorphism

KW - non-transversal points

KW - multidimentional diffeomophisms

KW - non-transversal homoclinic point

KW - Stability

KW - characteristic exponents separated from zero

UR - https://link.springer.com/article/10.1134/S1063454119040125

M3 - Article

VL - 52

SP - 380

EP - 387

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 4

ER -