Bibliographic Details
| Title: |
Semigroup Actions of Expanding Maps. |
| Authors: |
Carvalho, Maria1 mpcarval@fc.up.pt, Rodrigues, Fagner2 fagnerbernardini@gmail.com, Varandas, Paulo3 paulo.varandas@ufba.br |
| Source: |
Journal of Statistical Physics. Jan2017, Vol. 166 Issue 1, p114-136. 23p. |
| Subjects: |
Ruelle operators, Zeta functions, Thermodynamic equilibrium, Semigroup algebras, Topological entropy, Ergodic theory |
| Abstract: |
We consider semigroups of Ruelle-expanding maps, parameterized by random walks on the free semigroup, with the aim of examining their complexity and exploring the relation between intrinsic properties of the semigroup action and the thermodynamic formalism of the associated skew-product. In particular, we clarify the connection between the topological entropy of the semigroup action and the growth rate of the periodic points, establish the main properties of the dynamical zeta function of the semigroup action and relate these notions to recent research on annealed and quenched thermodynamic formalism. Meanwhile, we examine how the choice of the random walk in the semigroup unsettles the ergodic properties of the action. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
