In this work we relate the spectral properties of some transfer operators associated to piecewise Holder expanding maps to the statistical properties of the systems, such as existence of invariant measures and mixing. We obtain an unconditional estimate, which is optimal in some cases, for the radius of the essential spectrum (complement of the "compact part") of these operators acting on fractional Sobolev spaces. In addition, under a new small boundary pressure condition, we improve the estimate by establishing a variational principle for piecewise expanding maps and subadditive potentials. This is a joint work with Viviane Baladi.
Thermodynamic formalism for piecewise expanding maps in finite dimension
22.06.2023 15:00 - 15.06.2023 17:00
Organiser:
H. Bruin, R. Zweimüller
Location: