An interval map with aspectral gap on Lipschitz functions, but not on bounded variationfunctions

Sébastien Gouëzel

doi:10.3934/dcds.2009.24.1205

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2009, Volume 24, Issue 4: 1205-1208. Doi: 10.3934/dcds.2009.24.1205

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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

Received: June 30, 2008

Revised: November 30, 2008

Published: October 2009

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Abstract

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.

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Mathematics Subject Classification: 37E05, 37D20.

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

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