A variational principle for free semigroup actions

作者：Carvalho Maria^*; Rodrigues Fagner B; Varandas Paulo

来源：Advances in Mathematics, 2018, 334: 450-487.

DOI：10.1016/j.aim.2018.06.010

• Semigroup actions
• Expanding maps
• Skew-product
• Entropy

In this paper we introduce a notion of measure theoretical entropy for a finitely generated free semigroup action and establish a variational principle when the semigroup is generated by continuous self maps on a compact metric space and has finite topological entropy. In the case of semigroups generated by Ruelle-expanding maps we prove the existence of equilibrium states and describe some of their properties. Of independent interest are the different ways we will present to compute the metric entropy and a characterization of the stationary measures.

• 出版日期2018-8-20