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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

Sébastien Gouëzel 1,

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.
Keywords: bounded variation functions., spectral gap, Lipschitz functions, Transfer operator.
Mathematics Subject Classification: 37E05, 37D2.
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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