On dynamic properties of diffeomorphisms with homoclinic tangency

S. V. Gonchenko, D. V. Turaev, L. P. Shil'nikov

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

We study dynamic properties of systems in Newhouse domains near a diffeomorphism having a saddle fixed point with a homoclinic tangency in the following cases: one-dimensional, two-dimensional, where a fixed point is a saddle-focus with one real and two complex-conjugate multipliers, and four-dimensional saddle-focus with two pairs of complex-conjugate multipliers.

Original languageEnglish
Pages (from-to)1317-1343
Number of pages27
JournalJournal of Mathematical Sciences
Volume126
Issue number4
StatePublished - 1 Jan 2005

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (all)
  • Applied Mathematics

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