17 citations · 92 across the 15 of their papers we have counts for
17 papers
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…
Exponential mixing for singular skew-products
Oliver Butterley
We study skew-products of the form where is a non-uniformly expanding map on a manifold and is piecewise $\mathcal{C}…
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…
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…
Discontinuities cause essential spectrum
Oliver Butterley, Giovanni Canestrari, Sakshi Jain
We study transfer operators associated to piecewise monotone interval transformations and show that the essential spectrum is large whenever the Banach space bounds and…
Locating Ruelle-Pollicott resonances
Oliver Butterley, Niloofar Kiamari, Carlangelo Liverani
We study the spectrum of transfer operators associated to various dynamical systems. Our aim is to obtain precise information on the discrete spectrum. To this end we propose a uni…
Parabolic Flows Renormalized by Partially Hyperbolic Maps
Oliver Butterley, Lucia D. Simonelli
We consider parabolic flows on 3-dimensional manifolds which are renormalized by circle extensions of Anosov diffeormorphisms. This class of flows includes nilflows on the Heisenbe…
Polynomial decay of correlations for flows, including Lorentz gas examples
Peter Balint, Oliver Butterley, Ian Melbourne
We prove sharp results on polynomial decay of correlations for nonuniformly hyperbolic flows. Applications include intermittent solenoidal flows and various Lorentz gas models incl…
Open Sets of Exponentially Mixing Anosov Flows
Oliver Butterley, Khadim War
We prove that an Anosov flow with stable bundle mixes exponentially whenever the stable and unstable bundles are not jointly integrable. This allows us to show th…
Disintegration of Invariant Measures for Hyperbolic Skew Products
Oliver Butterley, Ian Melbourne
We study hyperbolic skew products and the disintegration of the SRB measure into measures supported on local stable manifolds. Such a disintegration gives a method for passing from…
Exponential Mixing for Skew Products with Discontinuities
Oliver Butterley, Peyman Eslami
We consider the skew product , where the base map is piecewise , covering and uniformly…
A Note on Operator Semigroups Associated to Chaotic Flows
Oliver Butterley
The transfer operator associated to a flow (continuous time dynamical system) is a one-parameter operator semigroup. We consider the operator-valued Laplace transform of this one-p…
Open sets of Axiom A flows with Exponentially Mixing Attractors (with Erratum)
Vítor Araújo, Oliver Butterley, Paulo Varandas
For any dimension we construct -open subsets of the space of vector fields such that the flow associated to each vector field is Axiom A and exhibits a non…
Area expanding C^{1+α} Suspension Semiflows
Oliver Butterley
We study a large class of suspension semiflows which contains the Lorenz semiflows. This is a class with low regularity (merely C^{1+α}) and where the return map is discontinuous a…
Robustly invariant sets in fibre contracting bundle flows
Oliver Butterley, Carlangelo Liverani
We provide abstract conditions which imply the existence of a robustly invariant neighbourhood of a global section of a fibre bundle flow. We then apply such a result to the bundle…
Expanding Semiflows on Branched Surfaces and One-Parameter Semigroups of Operators
Oliver Butterley
We consider expanding semiflows on branched surfaces. The family of transfer operators associated to the semiflow is a one-parameter semigroup of operators. The transfer operators…
An Alternative Approach to Generalised BV and the Application to Expanding Interval Maps
Oliver Butterley
We introduce a family of Banach spaces of measures, each containing the set of measures with density of bounded variation. These spaces are suitable for the study of weighted trans…