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- W2107496301 abstract "Let $T$ be a tree, ${mathop{rm End}nolimits}(T)$ be the number of ends of $T$ and let $L(T)$ be the infimum of topological entropies of transitive maps of $T$. We give an elementary approach to the estimate that $L(T)ge (1/{mathop{rm End}nolimits} (T))log 2$. We also divide the set of all trees (up to homeomorphisms) into pairwise disjoint subsets ${cal P}(i)$, $iin {0}cupN$ and prove that $L(T)=(1/({mathop{rm End}nolimits} (T)-i))log 2$ if $Tin {cal P}(i)$ with $i=0,1$, and $L(T)le (text{respectively} =) (1/({mathop{rm End}nolimits} (T)-i))log 2$ if $Tin {cal P}(i)$ (respectively $Tin {cal P}'(i))$ with $ige 2$, where ${cal P}'(i)$ is an infinite subset of ${cal P}(i)$. Furthermore, we show that there is a tree $T$ such that the topological entropy of each transitive map of $T$ is larger than $L(T)$, and hence disprove a conjecture of Alseda et al (1997)." @default.
- W2107496301 created "2016-06-24" @default.
- W2107496301 creator A5037065410 @default.
- W2107496301 date "2000-02-01" @default.
- W2107496301 modified "2023-09-27" @default.
- W2107496301 title "Topological entropy of transitive maps of a tree" @default.
- W2107496301 doi "https://doi.org/10.1017/s0143385700000134" @default.
- W2107496301 hasPublicationYear "2000" @default.
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