13 citations · 46 across the 14 of their papers we have counts for
16 papers
On a family of singular potentials: Parameter dependence of thermodynamic characteristics
Philipp Gohlke, Georgios Lamprinakis, Jörg Schmeling
We consider the family of singular potentials , over the doubling map and we examine the dependence of several thermodynamic and mul…
Generalized Thue-Morse measures: spectral and fractal analysis
Philipp Gohlke, Marc Kesseböhmer, Tanja I. Schindler
We investigate a family of Riesz products and show that they can be regarded as diffraction measures of generalized Thue-Morse sequences, possibly over an infinite alphabet. These…
A classification of intrinsic ergodicity for recognisable random substitution systems
Philipp Gohlke, Andrew Mitchell
We study a class of dynamical systems generated by random substitutions, which contains both intrinsically ergodic systems and instances with several measures of maximal entropy. I…
Rauzy fractals of random substitutions
Philipp Gohlke, Andrew Mitchell, Dan Rust +1
We develop a theory of Rauzy fractals for random substitutions, which are a generalisation of deterministic substitutions where the substituted image of a letter is determined by a…
Orbit separation dimension as complexity measure for primitive inflation tilings
Michael Baake, Franz Gähler, Philipp Gohlke
Orbit separation dimension (OSD), previously introduced as amorphic complexity, is a powerful complexity measure for topological dynamical systems with pure-point spectrum. Here, w…
Spectral theory of regular sequences: parametrisation and spectral characterisation
Michael Coons, James Evans, Philipp Gohlke +1
We extend the existence of ghost measures beyond nonnegative primitive regular sequences to a large class of nonnegative real-valued regular sequences. In the general case, where t…
Fast dimension spectrum for a potential with a logarithmic singularity
Philipp Gohlke, Georgios Lamprinakis, Jörg Schmeling
We regard the classic Thue--Morse diffraction measure as an equilibrium measure for a potential function with a logarithmic singularity over the doubling map. Our focus is on unusu…
Spectral Characteristics of Schrödinger Operators Generated by Product Systems
David Damanik, Jake Fillman, Philipp Gohlke
We study ergodic Schrödinger operators defined over product dynamical systems in which one factor is periodic and the other factor is either a subshift over a finite alphabet or an…
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…
Zero Measure Spectrum for Multi-Frequency Schrödinger Operators
Jon Chaika, David Damanik, Jake Fillman +1
Building on works of Berthé--Steiner--Thuswaldner and Fogg--Nous we show that on the two-dimensional torus, Lebesgue almost every translation admits a natural coding such that the…
On a family of singular continuous measures related to the doubling map
Michael Baake, Michael Coons, James Evans +1
Here, we study some measures that can be represented by infinite Riesz products of 1-periodic functions and are related to the doubling map. We show that these measures are purely…
Spectral properties of Schrödinger operators associated to almost minimal substitution systems
Benjamin Eichinger, Philipp Gohlke
We study the spectral properties of ergodic Schrödinger operators that are associated to a certain family of non-primitive substitutions on a binary alphabet. The corresponding sub…
Inflation word entropy for semi-compatible random substitutions
Philipp Gohlke
We introduce the concept of inflation word entropy for random substitutions with a constant and primitive substitution matrix. Previous calculations of the topological entropy of s…
Ergodic frequency measures for random substitutions
Philipp Gohlke, Timo Spindeler
We construct a family of ergodic measures on random substitution subshifts (RS-subshifts) associated to a primitive random substitution. In particular, the word frequencies of ever…
Scaling properties of the Thue--Morse measure
Michael Baake, Philipp Gohlke, Marc Kesseböhmer +1
The classic Thue--Morse measure is a paradigmatic example of a purely singular continuous probability measure on the unit interval. Since it has a representation as an infinite Rie…
Shifts of finite type and random substitutions
Philipp Gohlke, Dan Rust, Timo Spindeler
We prove that every topologically transitive shift of finite type in one dimension is topologically conjugate to a subshift arising from a primitive random substitution on a finite…