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Discontinuities cause essential spectrum on surfaces
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Discontinuities cause essential spectrum on surfaces
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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 acts on a Banach space with norm that is stronger than \(L^\infty\) or \(BV\). Three classes of examples are introduced and studied, both expanding and partially expanding. In two dimensions there is complication due to the geometry of the discontinuities, an issue not present in the one-dimensional case and which is explored in this work.
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Cited by 1 Pith paper
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Horocycle flows on abelian covers of surfaces of negative curvature
Establishes asymptotic ergodic integrals for horocycle flows on abelian covers of negative-curvature surfaces and a power deviation estimate on compact surfaces without pinching.
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