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math.DS2026
Anisotropic spaces and nil-automorphisms
Oliver Butterley, Minsung Kim
We introduce a family of geometric anisotropic Banach spaces on Heisenberg nilmanifolds and study the spectrum of the composition operator associated to partially hyperbolic automo…
math.DS2025
Discontinuous observables as an obstruction for small essential spectral radius
Oliver Butterley, Daniel Smania
We show that for a very wide class of Banach spaces of functions on [0,1] there are intrinsic lower bounds for the essential spectral radius of the transfer operator associated to…
math.DS2024
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…