Dynamical Morse entropy

Abstract

We consider actions of a tileable amenable group $\hat{I}“$ on a topological space $X$. For a continuous function on $X$, we define the entropy of the number of homologically detectable critical point of the average of that function over $\hat{I}“$. This number is bounded below by the sum of the Betti number entropy. This result is thus a generalization of a standard Morse inequality in differential geometry to this setting.

23 pages. This paper has been published in 2004 but was never posted on the arXiv