123 citations · 216 across the 9 of their papers we have counts for
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Rotation Sets and Topological Entropy for Random Circle Endomorphisms
Zixu Li, Simon Lloyd, Sergio Romaña
We study the topological dynamics of random circle endomorphisms of degree one over an ergodic measure-preserving dynamical system. Under an integrability assumption, we prove that…
Lift-Free Approaches to Random Rotation Number and Numerical Approximation
Zixu Li, Simon Lloyd
We study the random rotation number for random circle homeomorphisms. We introduce two new definitions of the random rotation number that can be stated without reference to any cho…
Periodicity and Rotation Number for Random Circle Homeomorphisms
Zixu Li, Simon Lloyd
We study discrete-time random dynamical systems where each fibre map is an orientation-preserving homeomorphism of the circle. We prove that the existence of a random periodic cycl…
A semi-invertible Oseledets Theorem with applications to transfer operator cocycles
Gary Froyland, Simon Lloyd, Anthony Quas
Oseledets' celebrated Multiplicative Ergodic Theorem (MET) is concerned with the exponential growth rates of vectors under the action of a linear cocycle on R^d. When the linear ac…
Coherent sets for nonautonomous dynamical systems
Gary Froyland, Simon Lloyd, Naratip Santitissadeekorn
We describe a mathematical formalism and numerical algorithms for identifying and tracking slowly mixing objects in nonautonomous dynamical systems. In the autonomous setting, such…
On the Closing Lemma problem for vector fields of bounded type on the torus
Simon Lloyd
We investigate the open Closing Lemma problem for vector fields on the 2-dimensional torus. Under the assumption of bounded type rotation number, the Closing Lemma is verifie…
Coherent structures and isolated spectrum for Perron-Frobenius cocycles
Gary Froyland, Simon Lloyd, Anthony Quas
We present an analysis of one-dimensional models of dynamical systems that possess 'coherent structures'; global structures that disperse more slowly than local trajectory separati…
Affine interval exchange transformations with flips and wandering intervals
C. Gutierrez, S. Lloyd, B. Pires
There exist uniquely ergodic affine interval exchange transformations of [0,1] with flips having wandering intervals and such that the support of the invariant measure is a Cantor…
Unique ergodicity of circle and interval exchange transformations with flips
C. Gutierrez, S. Lloyd, V. Medvedev +2
We study the existence of transitive exchange maps with flips defined on the unit circle. We provide a complete answer to the question of whether there exists a transitive exchange…