# Meeting Details

Title: Slow entropies, I: A slow introduction Working Seminar: Dynamics and its Working Tools Anatole Katok, Penn State Subexponential growth in topological and measurable dynamical systems can be quantified by using proper slow'' counterparts of the notions of topological and metric (Kolmogorov) entropy. The principal challenge here is that direct generalization fails and one has to use counterparts of non-standard definitions of the two entropies. Resulting notions are useful to produce interesting examples and counter-examples and they appeared intermittently starting from my 1977 paper on monotone (Kakutani) equivalence. Brief treatments of basic properties appeared in the 1997 paper joint with J.-P. Thouvenot and in the 2002 survey Principal structures'' joint with B. Hasselblatt. Other authors considered similar notions but no systematic treatment of the subject exists in the literature. Furthermore, relations between the slow entropy and other properties of dynamical systems remain mostly unexplored beyond few obvious remarks. This talk intends to provide a basic introduction to the subject and will be followed by other talks by the same speaker and by Jean-Paul Thouvenot at this seminar and possibly also at the Center for Dynamics and Geometry seminar.