On šilnikov′s homoclinic-saddle-focus theorem

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

Consideration is given to the chaotic dynamics near an orbit homoclinic to a saddle-focus fixed point of šilnikov type. A new type of symbolic system is used to describe the dynamics on the unstable manifold and its relation to the šilnikov dynamics. Techniques based on the šilnikov method are developed for this unifying treatment. These new ideas and techniques should be applicable for a wide variety of homoclinically and heteroclinically related problems.

Original languageEnglish (US)
Pages (from-to)305-329
Number of pages25
JournalJournal of Differential Equations
Volume102
Issue number2
DOIs
StatePublished - Apr 1993

Fingerprint

Homoclinic
Saddle
Unstable Manifold
Homoclinic Orbit
Chaotic Dynamics
Theorem
Fixed point
Orbits

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

On šilnikov′s homoclinic-saddle-focus theorem. / Deng, Bo.

In: Journal of Differential Equations, Vol. 102, No. 2, 04.1993, p. 305-329.

Research output: Contribution to journalArticle

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