TITLE:
The positive entropy kernel for some families of trees
2007 Nonlinearity, 20 (8), pp 1955--1967


AUTHORS:
Esther Barrabes i David Juher
Departament d'Informatica i Matematica Aplicada
Universitat de Girona
Ed. P-IV, Campus Montilivi
17071 Girona
E-mails: barrabes@ima.udg.edu, juher@ima.udg.edu

ABSTRACT:
The fact that a continuous self-map of a tree
has positive topological entropy is related to the amount of different
gods (greatest odd divisors) exhibited by its set of periods. Llibre
and Misiurewicz (1993))  and Blokh (1992) give generic upper bounds
for the maximum number of gods that a zero entropy tree map $\map{f}{T}$ can
exhibit, in terms of the number of endpoints and edges of $T$. In this paper
we compute exactly the minimum of the positive integers $n$ such that the
entropy of each tree map $\map{f}{T}$ exhibiting more than $n$ gods is
necessarily positive, for the family of trees which have a subinterval
containing all the branching points (this family includes the interval and
the stars). We also compute which gods are admissible for such maps.