# American Institute of Mathematical Sciences

November  2009, 24(4): 1205-1208. doi: 10.3934/dcds.2009.24.1205

## An interval map with a spectral gap on Lipschitz functions, but not on bounded variation functions

 1 IRMAR, Université de Rennes 1, 35042 Rennes, France

Received  July 2008 Revised  December 2008 Published  May 2009

We construct a uniformly expanding map of the interval, preserving Lebesgue measure, such that the corresponding transfer operator admits a spectral gap on the space of Lipschitz functions, but does not act continuously on the space of bounded variation functions.
Citation: Sébastien Gouëzel. An interval map with a spectral gap on Lipschitz functions, but not on bounded variation functions. Discrete and Continuous Dynamical Systems, 2009, 24 (4) : 1205-1208. doi: 10.3934/dcds.2009.24.1205
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