Tomasz Downarowicz


Title: Entropy structure

Abstract:
Investigating the relation between entropy and resolution, we propose an 
"entropy structure"
as a kind of master invariant for the entropy theory of topological 
dynamical systems. For this
we consider up to certain equivalence relation (capturing the "type of 
non-uniformity in convergence")
sequences of functions $(h_k)_k$ on the simplex of invariant measures, 
converging to the entropy
function $h$. An entropy structure recovers several existing invariants, 
including symbolic extension
entropy $\bold h_{sex}$ and the Misiurewicz parameter $\bold h^*$. 
Entropy theories by Misiurewicz,
Katok, Brin-Katok, Newhouse, Romagnoli, Ornstein-Weiss and others all 
yield candidate sequences
$(h_k)_k$; we determine which of these exhibit the correct type of 
convergence and hence become
entropy structures.