Dynamical phenomena in systems with structurally unstable Poincaré homoclinic orbits

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

Research output: Contribution to journalArticlepeer-review

100 Scopus citations


Recent results describing non-trivial dynamical phenomena in systems with homoclinic tangencies are represented. Such systems cover a large variety of dynamical models known from natural applications and it is established that so-called quasiattractors of these systems may exhibit rather non-trivial features which are in a sharp distinction with that one could expect in analogy with hyperbolic or Lorenz-like attractors. For instance, the impossibility of giving a finite-parameter complete description of dynamics and bifurcations of the quasiattractors is shown. Besides, it is shown that the quasiattractors may simultaneously contain saddle periodic orbits with different numbers of positive Lyapunov exponents. If the dimension of a phase space is not too low (greater than four for flows and greater than three for maps), it is shown that such a quasiattractor may contain infinitely many coexisting strange attractors.

Original languageEnglish
Pages (from-to)15-31
Number of pages17
Issue number1
StatePublished - 1 Jan 1996
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics


Dive into the research topics of 'Dynamical phenomena in systems with structurally unstable Poincaré homoclinic orbits'. Together they form a unique fingerprint.

Cite this