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arXiv · 1410.2199

Expanding and expansive time-dependent dynamics

Christoph Kawan
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Abstract

In this paper, time-dependent dynamical systems given by sequences of maps are studied. For systems built from expanding C^2-maps on a compact Riemannian manifold M with uniform bounds on expansion factors and derivatives, we provide formulas for the metric and topological entropy. If we only assume that the maps are C^1, but act in the same way on the fundamental group of M, we can show the existence of an equi-conjugacy to an autonomous system, implying a full variational principle for the entropy. Finally, we introduce the notion of strong uniform expansivity that generalizes the classical notion of positive expansivity, and we prove time-dependent analogues of some well-known results. In particular, we generalize Reddy's result which states that a positively expansive system locally expands distances in an equivalent metric.

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Christoph Kawan. 2015-01-26. Expanding and expansive time-dependent dynamics. https://doi.org/10.1088/0951-7715%2F28%2F3%2F669

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