Multidimensional diffeomorphisms with stable periodic points

Результат исследований: Научные публикации в периодических изданияхстатьярецензирование

Аннотация

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.

Язык оригиналаанглийский
Страницы (с-по)808-810
Число страниц3
ЖурналDoklady Mathematics
Том84
Номер выпуска3
DOI
СостояниеОпубликовано - 1 дек 2011

Предметные области Scopus

  • Математика (все)

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