非自治动力系统的原像熵

本文对紧致度量空间上的连续自映射序列应用生成集和分离集引入了点原像熵、原像分枝熵以及原像关系熵等几类原像熵的定义并进行了研究.主要结果是:(1) 证明了这些熵都是等度拓扑共轭不变量.(2)讨论了这些原像熵之间及它们与拓扑熵之间的关系,得到了联系这些熵的不等式.(3)证明了对正向可扩的连续自映射序列而言, 两类点原像熵相等,原像分枝熵与原像关系熵也相等.(4)证明了对(a).由闭Riemann 流形上的一个扩张映射经充分小的C1-扰动生成的自映射序列,以及(b).有限图上等度连续的自映射序列,有零原像分枝熵.

Preimage Entropies of Nonautonomous Dynamical Systems

In this paper, four entropy-like invariants for nonautonomous discrete dynamical systems given by a sequence of continuous selfmaps of a compact metric space are introduced and studied. The main results are: (1) these entropies are all invariant with respect to equiconjugacy. (2) the relations between these entropies are established. (3) for positively expansive nonautonomous systems, two types of pointwise preimage entropies are equal, and the preimage branch entropy and the preimage relation entropy are equal too. (4) two classes of nonautonomous systems: (a), a sequence of small C1-perturbations of an expanding map on a closed Riemmanian manifold, and (b). a sequence of equicontinuous maps defined on a finite graph, have zero preimage branch entropy.