A note on the periodic orbits and topological entropy of graph maps [ Back ]

Date:
07.05.01   
Times:
16:00
Place:
Centre de Recerca Matemàtica
Speaker:
David Juher
University:
UdG

Abstract

For a continuous map f on the interval, to each periodic orbit P of f we can associate a number h(P) which is the topological entropy of the connect-the-dots map corresponding to P (or the linearization of P). In fact, h(P) corresponds to the infimum of the entropies of all maps exhibiting orbits with the same combinatorics as P. Takahashi′s formula states that the entropy of f is the supremum of the values h(P) corresponding to all the periodic orbits P of f (furthermore, for each n, we can take the supremum only over the orbits whose size is greater than n). We show that an analogous relation between periodic behavior and topological entropy is satisfied for continuous maps on graphs.