Year: 2015
Type: article
Abstract: In this paper, time-dependent dynamical systems given by sequences of maps are studied. For systems built from expanding -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 , 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.
Source: Nonlinearity
Author: Christoph Kawan
Institution: University of Passau
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W2006368549