TY - JOUR

T1 - Smooth diffeomorphisms with countable set of stable periodic points

AU - Vasil'Eva, E. V.

PY - 2011/8/1

Y1 - 2011/8/1

N2 - Smooth diffeomorphisms with countable set of stable periodic points are presented. A neighborhood of a homoclinic point may contain infinitely many stable periodic points, but at least one characteristic exponent of such points tends to zero with increasing the period. By Rolle's theorem, the second derivative of g vanishes at the points. Similarly, it is easy to see that the derivative of any order higher than the second of the function g vanishes at infinitely many points in any neighborhood of zero. Conditions were obtained under which any neighborhood of a homoclinic point of a diffeomorphism contains infinitely many stable periodic points whose characteristic exponents are bounded away from zero.

AB - Smooth diffeomorphisms with countable set of stable periodic points are presented. A neighborhood of a homoclinic point may contain infinitely many stable periodic points, but at least one characteristic exponent of such points tends to zero with increasing the period. By Rolle's theorem, the second derivative of g vanishes at the points. Similarly, it is easy to see that the derivative of any order higher than the second of the function g vanishes at infinitely many points in any neighborhood of zero. Conditions were obtained under which any neighborhood of a homoclinic point of a diffeomorphism contains infinitely many stable periodic points whose characteristic exponents are bounded away from zero.

UR - http://www.scopus.com/inward/record.url?scp=80655125456&partnerID=8YFLogxK

U2 - 10.1134/S1064562411030252

DO - 10.1134/S1064562411030252

M3 - Article

AN - SCOPUS:80655125456

VL - 84

SP - 441

EP - 443

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - 1

ER -