Topological entropy of transitive maps of a tree

Authors
Citation
Xd. Ye, Topological entropy of transitive maps of a tree, ERGOD TH DY, 20, 2000, pp. 289-314
Citations number
18
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics
Journal title
ERGODIC THEORY AND DYNAMICAL SYSTEMS
ISSN journal
0143-3857 → ACNP
Volume
20
Year of publication
2000
Part
1
Pages
289 - 314
Database
ISI
SICI code
0143-3857(200002)20:<289:TEOTMO>2.0.ZU;2-8
Abstract
Let T be a tree, End(T) be the number of ends of T and let L(T) be the infi mum of topological entropies of transitive maps of T. We give an elementary approach to the estimate that L(T) greater than or equal to (1/End(T)) log 2. We also divide the set of all trees (up to homeomorphisms) into pairwise disjoint subsets P(i), i is an element of {0} boolean OR N and prove that L(T) = (1/(End(T) - i))log2 if T is an element of P(i) with i = 0, i, and L (T) less than or equal to (respectively =) (1/(End(T) - i))log2 if T is an element of P(i) (respectively T is an element of P'(i)) with i greater than or equal to 2, where P'(i) is an infinite subset of P(i). Furthermore, we show that there is a tree T such that the topological entropy of each trans itive map of T is larger than L(T), and hence disprove a conjecture of Alse da et al (1997).