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1 ENTROPY OF DYNAMICAL SYSTEMS WITH REPETITION PROPERTY

By Wen Huang, Leiye Xu and Yingfei Yi

Abstract

Abstract. The repetition property of a dynamical system, a notion introduced in [2], plays an importance role in analyzing spectral properties of ergodic Schrödinger operators. In this paper, entropy of dynamical systems with repetition property is investigated. It is shown that the topological entropy of dynamical systems with the global repetition property is zero. Minimal dynamical systems having both topological repetition property and positive topological entropy are constructed. This provides a class of ergodic Schrödinger operators with potentials generated by positive entropy minimal dynamical systems that, in contrast to common beliefs, admit no eigenvalues. 1

Year: 2011
OAI identifier: oai:CiteSeerX.psu:10.1.1.187.3269
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