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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm110-2-7,
author = {Andrzej Bi\'s},
title = {Partial variational principle for finitely generated groups of polynomial growth and some foliated spaces},
journal = {Colloquium Mathematicae},
volume = {111},
year = {2008},
pages = {431-449},
zbl = {1142.28300},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm110-2-7}
}
Andrzej Biś. Partial variational principle for finitely generated groups of polynomial growth and some foliated spaces. Colloquium Mathematicae, Tome 111 (2008) pp. 431-449. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm110-2-7/