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math.DS2023★ 2 cited
Discontinuities cause essential spectrum on surfaces
Oliver Butterley, Giovanni Canestrari, Roberto Castorrini
Two-dimensional maps with discontinuities are considered. It is shown that, in the presence of discontinuities, the essential spectrum of the transfer operator is large whenever it…
math.DS2023★ 2 cited
Thermodynamic formalism for piecewise expanding maps in finite dimension
Viviane Baladi, Roberto Castorrini
We study weighted transfer operators associated to a piecewise expanding map on a compact manifold, and a piecewise Holder weight, acting on Sobolev spaces. We bound the essential…