On models with non-rough Poincaré homoclinic curves

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

Research output: Contribution to journalArticlepeer-review

88 Scopus citations


The possibility of an a priori complete description of finite-parameter models including systems with structurally unstable Poincaré homoclinic curves is studied. The main result reported here is that systems having a countable set of moduli of ω-equivalence and systems having infinitely many degenerate periodic and homoclinic orbits are dense in the Newhouse regions of ω-non-stability. We discuss the question of correctly setting a problem for the analysis of models of such type.

Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalPhysica D: Nonlinear Phenomena
Issue number1-4
StatePublished - 30 Jan 1993
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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