Chaos in periodically forced reversible vector fields

Isabel S. Labouriau and Elisa Sovrano

Journal of Singularities
volume 22 (2020), 227-240

Received: 25 January 2019. Received in revised form: 8 July 2020.

DOI: 10.5427/jsing.2020.22p

Add a reference to this article to your citeulike library.

Abstract:

We discuss the appearance of chaos in time-periodic perturbations of reversible vector fields in the plane. We use the normal forms of codimension 1 reversible vector fields and discuss the ways a time-dependent periodic forcing term of pulse form may be added to them to yield topological chaotic behaviour. Chaos here means that the resulting dynamics is semiconjugate to a shift in a finite alphabet. The results rely on the classification of reversible vector fields and on the theory of topological horseshoes. This work is part of a project of studying periodic forcing of symmetric vector fields.

2010 Mathematical Subject Classification:

34C28, 37G05, 37G40, 54H20

Key words and phrases:

Reversible fields, Symbolic dynamics, Topological horseshoes

Author(s) information:

Isabel S. Labouriau
Centro de Matemática da Universidade do Porto
Rua do Campo Alegre 687
4169-007 Porto, Portugal
email: islabour@fc.up.pt

Elisa Sovrano
École des Hautes Études en Sciences Sociales
Centro de Matemática da Universidade do Porto
Present address:
Centre d' €Analyse et de Mathématique Sociales (CAMS)
CNRS, 54 Boulevard Raspail, 75006, Paris, France
email: elisa.sovrano@ehess.fr