Existence of heterodimensional cycles near shilnikov loops in systems with A Z2 symmetry

Dongchen Li, Dmitry V. Turaev

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We prove that a pair of heterodimensional cycles can be born at the bifurcations of a pair of Shilnikov loops (homoclinic loops to a saddle-focus equilibrium) having a one-dimensional unstable manifold in a volume-hyperbolic flow with a ℤ2 symmetry. We also show that these heterodimensional cycles can belong to a chain-transitive attractor of the system along with persistent homoclinic tangency.

Original languageEnglish
Pages (from-to)4399-4437
Number of pages39
JournalDiscrete and Continuous Dynamical Systems
Volume37
Issue number8
DOIs
StatePublished - 1 Aug 2017
Externally publishedYes

Keywords

  • Chaotic dynamics
  • Heterodimensional cycle
  • Homoclinic bifurcation
  • Homoclinic tangency
  • Saddle-focus
  • Strange attractor

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