6533b7ddfe1ef96bd1273d00
RESEARCH PRODUCT
Markov extensions for multi-dimensional dynamical systems
Jérôme Buzzisubject
Pure mathematicsmedicine.medical_specialtyGeneral MathematicsPrinciple of maximum entropyMathematical analysisMeasure-preserving dynamical systemTopological dynamicsTopological entropyTopological entropy in physicsMaximum entropy probability distributionmedicineEntropy rateJoint quantum entropyMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1999-12-01 | Israel Journal of Mathematics |