Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Exponential decay of Lebesgue numbers

Pages: 3773 - 3785, Volume 32, Issue 10, October 2012      doi:10.3934/dcds.2012.32.3773

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Peng Sun - China Economics and Management Academy, Central University of Finance and Economics, No. 39 College South Road, Beijing, 100081, China (email)

Abstract: We study the exponential rate of decay of Lebesgue numbers of open covers in topological dynamical systems. We show that topological entropy is bounded by this rate multiplied by dimension. Some corollaries and examples are discussed.

Keywords:  Lebesgue number, topological entropy, box dimension, Hausdorff dimension, Lipschitz constant, open cover, exponential decay.
Mathematics Subject Classification:  Primary: 37B40, 54E45, 54F45.

Received: January 2011;      Revised: March 2012;      Available Online: May 2012.