Chaotic double cycling

• Type: Article in International Scientific Journal
• Date: 2011

Authors

Alexandre A P Rodrigues (Author) Other; Isabel S Labouriau (Author) FCUP; Manuela A D Aguiar (Author) FEP

Journal

Title: Dynamical Systems

Vol. 26 No. 2

Pages: 199-233

ISSN: 1468-9367

Publisher: Taylor & Francis

Indexing

ISI Web of Knowledge - 16 Citations

ISI Web of Science

Scopus - 15 Citations

SciELO - Scientific Electronic Library Online

Scientific classification

FOS: Engineering and technology > Mechanical engineering

CORDIS: Physical sciences > Mathematics

Other information

Authenticus ID: P-002-YBY

DOI: 10.1080/14689367.2011.557179

Abstract (EN): We study the dynamics of a generic vector field in the neighbourhood of a heteroclinic cycle of non-trivial periodic solutions whose invariant manifolds meet transversely. The main result is the existence of chaotic double cycling: there are trajectories that follow the cycle making any prescribed number of turns near the periodic solutions, for any given bi-infinite sequence of turns. Using symbolic dynamics, arbitrarily close to the cycle, we find a robust and transitive set of initial conditions whose trajectories follow the cycle for all time and that is conjugate to a Markov shift over a finite alphabet. This conjugacy allows us to prove the existence of infinitely many heteroclinic and homoclinic subsidiary connections, which give rise to a heteroclinic network with infinitely many cycles and chaotic dynamics near them, exhibiting themselves switching and cycling. We construct an example of a vector field with Z3 symmetry in a five-dimensional sphere with a heteroclinic cycle having this property.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 35