Multidimentional Diffeomorphisms with Stable Periodic Points

Research output: Contribution to journalArticlepeer-review

Abstract

The conditions are obtained for the existence of an infinite set of stable periodic
points 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.
Original languageEnglish
Pages (from-to)380-387
JournalVestnik St. Petersburg University: Mathematics
Volume52
Issue number4
Early online date23 Dec 2019
StatePublished - 2019

Scopus subject areas

  • Mathematics(all)

Keywords

  • multidimentional diffeomophisms
  • non-transversal homoclinic point
  • Stability
  • characteristic exponents separated from zero

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