Expanding and expansive time-dependent dynamics
Expanding and expansive time-dependent dynamics
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DOI：
10.1088/0951-7715/28/3/669
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发表时间：
2014-10
期刊：
影响因子：
1.7
通讯作者：
C. Kawan
中科院分区：
文献类型：
--
作者：
C. Kawan
本文研究由映射序列给出的含时动力系统。对于由紧致黎曼流形M上的扩张映射建立的系统，在扩张因子和导数上具有一致的界，我们给出了度量和拓扑熵的公式。如果我们只假设映射是，但以相同的方式作用在M的基本群上，我们可以证明自治系统的等共轭性的存在，这意味着熵的完全变分原理。最后，我们引入了强一致膨胀性的概念，推广了经典的正膨胀性的概念，我们证明了一些著名的结果依赖于时间的类似物。特别地，我们推广了Reddy的结果，该结果表明，一个正扩张系统在一个等价的度量中局部扩展距离。
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.