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

Sébastien Gouëzel (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Domaines: Systèmes dynamiques [math.DS]

Sébastien Gouëzel. An interval map with a spectral gap on Lipschitz functions, but not on bounded variation functions. Discrete and Continuous Dynamical Systems - Series S, 2009, 24 (4), pp.1205-1208. ⟨10.3934/dcds.2009.24.1205⟩. ⟨hal-00318066⟩