The essential coexistence phenomenon in dynamics

摘要

This article is a survey of recent results on the essential coexistence of hyperbolic and non-hyperbolic behaviour in dynamics. Though in the absence of a general theory, the coexistence phenomenon has been shown in various systems during the last three decades. We will describe the contemporary state of the art in this area with emphasis on some new examples in smooth conservative systems, in both cases of discrete and continuous-time.