Esther Barrabés and David Juher 2007 Nonlinearity 20 1955 doi:10.1088/0951-7715/20/8/008
The positive entropy kernel for some families of trees
Esther Barrabés and David Juher
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The fact that a continuous self-map of a tree has positive topological entropy is related to the number of different greatest odd divisors (gods) exhibited by its set of periods. Llibre and Misiurewicz (1993 Topology 32 649–64) and Blokh (1992 Nonlinearity 5 1375–82) give generic upper bounds for the maximum number of gods that a zero entropy tree map f: T → 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 f: T → 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.
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Issue 8 (August 2007)
Received 27 December 2006, in final form 4 June 2007
Published 10 July 2007
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The positive entropy kernel for some families of trees
Esther Barrabés and David Juher 2007 Nonlinearity 20 1955
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