19 citations · 57 across the 15 of their papers we have counts for
18 papers
Intermediate -shifts as greedy -shifts with a hole
Niels Langeveld, Tony Samuel
We show that every intermediate -transformation is topologically conjugate to a greedy -transformation with a hole at zero, and provide a counterexample illustrating that the…
Measure theoretic entropy of random substitution subshifts
Philipp Gohlke, Andrew Mitchell, Dan Rust +1
Subshifts of deterministic substitutions are ubiquitous objects in dynamical systems and aperiodic order (the mathematical theory of quasicrystals). Two of their most striking feat…
Periodic intermediate -expansions of Pisot numbers
Blaine Quackenbush, Tony Samuel, Matthew A. West
The subshift of finite type property (also known as the Markov property) is ubiquitous in dynamical systems and the simplest and most widely studied class of dynamical systems are…
Generalised Krein-Feller operators and gap diffusions via transformations of measure spaces
Marc Kesseböhmer, Aljoscha Niemann, Tony Samuel +1
We consider the generalised Krein-Feller operator with respect to compactly supported Borel probability measures and with the natural restrictions that is a…
On the continuity of entropy of Lorenz maps
Zoe Cooperband, Erin P. J. Pearse, Blaine Quackenbush +3
We consider a one parameter family of Lorenz maps indexed by their point of discontinuity and constructed from a pair of bilipschitz functions. We prove that their topological…
Diffraction of return time measures
Marc Kesseböhmer, Arne Mosbach, Tony Samuel +1
Letting denote an ergodic transformation of the unit interval and letting denote an observable, we construct the -weighted return time measure…
The Sierpiński gasket as the Martin boundary of a non-isotropic Markov chain
Marc Kesseböhmer, Tony Samuel, Karenina Sender
In 2012 Lau and Ngai, motivated by the work of Denker and Sato, gave an example of an isotropic Markov chain on the set of finite words over a three letter alphabet, whose Martin b…
On the density of intermediate β-shifts of finite type
Bing Li, Tuomas Sahlsten, Tony Samuel +1
We determine the structure of the set of intermediate -shifts of finite type. Specifically, we show that this set is dense in the parameter space $Δ= \{ (β, α) \in \mathbb{R}^{2…
Regularity of aperiodic minimal subshifts
Fabian Dreher, Marc Kesseböhmer, Arne Mosbach +2
At the turn of this century Durand, and Lagarias and Pleasants established that key features of minimal subshifts (and their higher-dimensional analogues) to be studied are linearl…
A classification of aperiodic order via spectral metrics and Jarník sets
Maik Gröger, Marc Kesseböhmer, Arne Mosbach +2
Given an and a with unbounded continued fraction entries, we characterise new relations between Sturmian subshifts with slope with respect to (i) an -Höder regula…
A note on measure-geometric Laplacians
Marc Kesseböhmer, Tony Samuel, Hendrik Weyer
We consider the measure-geometric Laplacians with respect to atomless compactly supported Borel probability measures as introduced by Freiberg and Zähle in 2002 and show…
On the convergence to equilibrium of unbounded observables under a family of intermittent interval maps
Johannes Kautzsch, Marc Kesseböhmer, Tony Samuel
We consider a family of Markov interval maps interpolating between the Tent map and the Farey map . Letti…
On the asymptotics of the -Farey transfer operator
Johannes Kautzsch, Marc Kesseböhmer, Tony Samuel +1
We study the asymptotics of iterates of the transfer operator for non-uniformly hyperbolic -Farey maps. We provide a family of observables which are Riemann integrable, locally…
Intermediate β-shifts of finite type
Bing Li, Tuomas Sahlsten, Tony Samuel
An aim of this article is to highlight dynamical differences between the greedy, and hence the lazy, -shift (transformation) and an intermediate -shift (transformation), for…
Continuous images of Cantor's ternary set
Fabian Dreher, Tony Samuel
The Hausdorff-Alexandroff Theorem states that any compact metric space is the continuous image of Cantor's ternary set . It is well known that there are compact Hausdorff spaces…
Embedding the symbolic dynamics of Lorenz maps
Tony Samuel, Nina Snigireva, Andrew Vince
Necessary and sufficient conditions for the symbolic dynamics of a Lorenz map to be fully embedded in the symbolic dynamics of a piecewise continuous interval map are given. As an…
A Simple Proof of Vitali's Theorem for Signed Measures
Tony Samuel
There are several theorems named after the Italian mathematician Vitali. In this note we provide a simple proof of an extension of Vitali's Theorem on the existence of non-measurab…
Spectral metric spaces for Gibbs measures
Marc Kesseböhmer, Tony Samuel
We construct spectral metric spaces for Gibbs measures on a one-sided topologically exact subshift of finite type. That is, for a given Gibbs measure we construct a spectral triple…