The essential coexistence phenomenon in dynamics. (English) Zbl 1287.37007
Summary: 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.
MSC:
| 37A25 | Ergodicity, mixing, rates of mixing |
| 37C40 | Smooth ergodic theory, invariant measures for smooth dynamical systems |
| 37D40 | Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) |
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