Periods implying almost all periods for tree maps

Academic Article

Abstract

  • Let X be a compact tree f:X to X be a continuous map and End(X) be the number of endpoints of X. The author proves the following: Theorem 1. Let X be a tree. Then the following holds. (i) Let n>1 be an integer with no ′ divisors less than or equal to End(X)+1. If a map f:X to X has a cycle of period n, then f has cycles of all periods greater than 2 End(X)(n-1). Moreover, h(f)>or=In2/(nEnd(X)-1). (ii) Let 10. Note that Misiurewicz's conjecture and the last result are true for graph maps; an alternative proof of the last result may be also found in a paper by Llibre and Misiurewicz (1991).
  • Published In

  • Nonlinearity  Journal
  • Digital Object Identifier (doi)

    Author List

  • Blokh AM
  • Start Page

  • 1375
  • End Page

  • 1382
  • Volume

  • 5
  • Issue

  • 6