Israel Journal of Mathematics

, Volume 112, Issue 1, pp 357–380

Markov extensions for multi-dimensional dynamical systems



By a result of F. Hofbauer [11], piecewise monotonic maps of the interval can be identified with topological Markov chains with respect to measures with large entropy. We generalize this to arbitrary piecewise invertible dynamical systems under the following assumption: the total entropy of the system should be greater than the topological entropy of the boundary of some reasonable partition separating almost all orbits. We get a sufficient condition for these maps to have a finite number of invariant and ergodic probability measures with maximal entropy. We illustrate our results by quoting an application to a class of multi-dimensional, non-linear, non-expansive smooth dynamical systems.


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© Hebrew University 1999

Authors and Affiliations

  1. 1.Laboratoire de TopologieUniversité de Bourgogne / CNRSDijon CedexFrance

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