Partial variational principle for finitely generated groups of polynomial growth and some foliated spaces
Volume 110 / 2008
Colloquium Mathematicum 110 (2008), 431-449
MSC: Primary 28A65; Secondary 37C85, 37B40.
DOI: 10.4064/cm110-2-7
Abstract
We generalize the notion of topological pressure to the case of a finitely generated group of continuous maps and introduce group measure entropy. Also, we provide an elementary proof that any finitely generated group of polynomial growth admits a group invariant measure and show that for a group of polynomial growth its measure entropy is less than or equal to its topological entropy. The dynamical properties of groups of polynomial growth are reflected in the dynamics of some foliated spaces.
