Chaotic double cycling

• Tipo: Artigo em Revista Científica Internacional
• Data: 2011

Autores

Alexandre A P Rodrigues (Autor) Outra; Isabel S Labouriau (Autor) FCUP; Manuela A D Aguiar (Autor) FEP

Revista

Título: Dynamical Systems

Vol. 26 Nº 2

Páginas: 199-233

ISSN: 1468-9367

Editora: Taylor & Francis

Indexação

ISI Web of Knowledge - 16 Citações

ISI Web of Science

Scopus - 15 Citações

SciELO - Scientific Electronic Library Online

Classificação Científica

FOS: Ciências da engenharia e tecnologias > Engenharia mecânica

CORDIS: Ciências Físicas > Matemática

Outras Informações

ID Authenticus: 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.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 35