Abstract

Entropy is an important notion for understanding the complexity of dynamical systems. Several important entropy-like invariants based on the preimage structure for noninvertible maps have been defined and studied by some authors. In this chapter, following the idea of Hurley, we first further study the relationship among the topological entropy, pseudo-orbit, and preimage entropies for topological dynamical systems from the view of localization. Secondly, two entropy-like invariants, which are called the partial entropy and bundle-like entropy, for nonautonomous discrete dynamical systems are introduced. A relationship between the topological entropy and such two entropies is established.

Keywords: topological entropy, point entropy, pseudo-orbit, partial entropy, bundle-like entropy

2000 Mathematics Subject Classification: Primary: 37B40, 37A35, 37B10, 37A05
