On intrinsic ergodicity and weakenings of the specification property.(English)Zbl 1358.37032
The author considers the problem of understanding what dynamical system with weaker conditions than specification, such as almost specification or nonuniform specification is intrinsically ergodic, i.e., it has a unique measure of maximal entropy. Specification property was introduced by Bowen, to specify prescribed orbits of points in the phase space by the orbit of a point with a “delayed” time \(M(\varepsilon)\) for any \(\varepsilon> 0\). For dynamical systems with the properties of expansiveness and specification there exists a unique measure of maximal entropy. Thus, an interesting problem is to analyze when weaker versions of the specification imply intrinsic ergodicity. The author proposes examples of subshifts with the properties of nonuniform and almost specification which possess more that one measure of maximal entropy.
Reviewer: Alejandro Mesón (La Plata)
MSC:
| 37B10 | Symbolic dynamics |
| 37B40 | Topological entropy |
| 37D35 | Thermodynamic formalism, variational principles, equilibrium states for dynamical systems |
| 37A35 | Entropy and other invariants, isomorphism, classification in ergodic theory |
| 37B05 | Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) |
Cite
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