2008, 2(2): 315-338. doi: 10.3934/jmd.2008.2.315

Growth and mixing

1. 

Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń

2. 

School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel

Received  August 2007 Revised  November 2007 Published  January 2008

Given a bi-Lipschitz measure-preserving homeomorphism of a finite dimensional compact metric measure space, consider the sequence of the Lipschitz norms of its iterations. We obtain lower bounds on the growth rate of this sequence assuming that our homeomorphism mixes a Lipschitz function. In particular, we get a universal lower bound which depends on the dimension of the space but not on the rate of mixing. Furthermore, we get a lower bound on the growth rate in the case of rapid mixing. The latter turns out to be sharp: the corresponding example is given by a symbolic dynamical system associated to the Rudin–Shapiro sequence
Citation: Krzysztof Frączek, Leonid Polterovich. Growth and mixing. Journal of Modern Dynamics, 2008, 2 (2) : 315-338. doi: 10.3934/jmd.2008.2.315
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