October  2012, 32(10): 3773-3785. doi: 10.3934/dcds.2012.32.3773

Exponential decay of Lebesgue numbers

1. 

China Economics and Management Academy, Central University of Finance and Economics, No. 39 College South Road, Beijing, 100081, China

Received  January 2011 Revised  March 2012 Published  May 2012

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.
Citation: Peng Sun. Exponential decay of Lebesgue numbers. Discrete and Continuous Dynamical Systems, 2012, 32 (10) : 3773-3785. doi: 10.3934/dcds.2012.32.3773
References:
[1]

R. Bowen, Topological entropy for noncompact sets, Trans. Amer. Math. Soc., 184 (1973), 125-136. doi: 10.1090/S0002-9947-1973-0338317-X.

[2]

X. Dai, Z. Zhou and X. Geng, Some relations between Hausdorff-dimensions and entropies, Sci. China Ser. A, 41 (1998), 1068-1075. doi: 10.1007/BF02871841.

[3]

A. Katok and B. Hasselblatt, "Introduction to the Modern Theory of Dynamical Systems," With a supplementary chapter by Katok and Leonardo Mendoza, Encyclopedia of Mathematics and its Applications, 54, Cambridge University Press, Cambridge, 1995.

[4]

M. Misiurewicz, On Bowen's definition of topological entropy, Discrete Contin. Dyn. Syst., 10 (2004), 827-833. doi: 10.3934/dcds.2004.10.827.

[5]

P. Sun, Exponential decay of expansive constants, preprint, 2011.

[6]

P. Walters, "An Introduction to Ergodic Theory," Graduate Texts in Mathematics, 79, Springer-Verlag, New York-Berlin, 1982.

show all references

References:
[1]

R. Bowen, Topological entropy for noncompact sets, Trans. Amer. Math. Soc., 184 (1973), 125-136. doi: 10.1090/S0002-9947-1973-0338317-X.

[2]

X. Dai, Z. Zhou and X. Geng, Some relations between Hausdorff-dimensions and entropies, Sci. China Ser. A, 41 (1998), 1068-1075. doi: 10.1007/BF02871841.

[3]

A. Katok and B. Hasselblatt, "Introduction to the Modern Theory of Dynamical Systems," With a supplementary chapter by Katok and Leonardo Mendoza, Encyclopedia of Mathematics and its Applications, 54, Cambridge University Press, Cambridge, 1995.

[4]

M. Misiurewicz, On Bowen's definition of topological entropy, Discrete Contin. Dyn. Syst., 10 (2004), 827-833. doi: 10.3934/dcds.2004.10.827.

[5]

P. Sun, Exponential decay of expansive constants, preprint, 2011.

[6]

P. Walters, "An Introduction to Ergodic Theory," Graduate Texts in Mathematics, 79, Springer-Verlag, New York-Berlin, 1982.

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