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arXiv · 1901.09009

Chaos in periodically forced reversible vector fields

Isabel S. Labouriau·Elisa Sovrano
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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 semi-conjugate 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.

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Isabel S. Labouriau, Elisa Sovrano. 2019-01-25. Chaos in periodically forced reversible vector fields. https://arxiv.org/abs/1901.09009

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