Resumen de Relative entropy, asymptotic pairs and chaos

Guohua Zhang

• In this paper, we prove that positive conditional entropy implies the existence of asymptotic pairs and scrambled sets on fibers. Moreover, we introduce the notion of conditional topological entropy for a subset using Bowen's definition of separated and spanning sets, and prove that the conditional topological entropy of a system relative to a factor is the supremum of conditional topological entropy of its scrambled sets on fibers.