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TOPOLOGICAL ENTROPY OF A SEQUENCE OF MONOTONE MAPS ON CIRCLES

  • Zhu Yuhun (College of Mathematics and Information Science Hebei Normal University) ;
  • Zhang Jinlian (College of Mathematics and Information Science Hebei Normal University) ;
  • He Lianfa (College of Mathematics and Information Science Hebei Normal University)
  • Published : 2006.03.01

Abstract

In this paper, we prove that the topological entropy of a sequence of equi-continuous monotone maps $f_{1,\infty}={f_i}\;\infty\limits_{i=1}$on circles is $h(f_{1,\infty})={\frac{lim\;sup}{n{\rightarrow}\infty}}\;\frac 1 n \;log\;{\prod}\limits_{i=1}^n|deg\;f_i|$. As applications, we give the estimation of the entropies for some skew products on annular and torus. We also show that a diffeomorphism f on a smooth 2-dimensional closed manifold and its extension on the unit tangent bundle have the same entropy.

Keywords

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