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

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

2008-09-03

arxiv.org/abs/0809.0658v1

Mathematics

Dynamical Systems

4 pages

Scientific paper

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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