Persistent heterodimensional cycles in periodic perturbations of Lorenz-like attractors

Dongchen Li, Dmitry Turaev

Research output: Contribution to journalArticlepeer-review

Abstract

We prove that heterodimensional cycles can be created by unfolding a pair of homoclinic tangencies in a certain class of C r-diffeomorphisms (r=3, ⋯, ∞,ω). This implies the existence of a C 2-open domain in the space of dynamical systems with a certain type of symmetry where systems with heterodimensional cycles are dense in C r. In particular, we describe a class of three-dimensional flows with a Lorenz-like attractor such that an arbitrarily small time-periodic perturbation of any such flow can belong to this domain - in this case the corresponding heterodimensional cycles belong to a chain-transitive attractor of the perturbed flow.

Original languageEnglish
Pages (from-to)971-1015
Number of pages45
JournalNonlinearity
Volume33
Issue number3
DOIs
StatePublished - 1 Jan 2020
Externally publishedYes

Keywords

  • Lorenz attractor
  • chaotic dynamics
  • heterodimensional cycle
  • homoclinic bifurcation
  • homoclinic tangency

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