Partial variational principle for finitely generated groups of polynomial growth and some foliated spaces

Volume 110 / 2008

Andrzej Biś Colloquium Mathematicum 110 (2008), 431-449 MSC: Primary 28A65; Secondary 37C85, 37B40. DOI: 10.4064/cm110-2-7


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.


  • Andrzej BiśFaculty of Mathematics
    University of Łódź
    Banacha 22
    90-238 Łódź, Poland

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