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).