4 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…
On uniform recurrence for hyperbolic automorphisms of the -dimensional torus
Georgios Lamprinakis, Tomas Persson, Alejandro Rodriguez Sponheimer
We are interested in studying sets of the form \[ \mathcal{U}(α) := \left\{ x\in X: \ \exists M=M(x) \geq 1 \text{ such that } \forall N\geq M, \ \exists n\leq N \text{ such that }…
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…
Joint invariant sets for non-commutative expanding Markov maps of the circle
Georgios Lamprinakis
A long-standing question is what invariant sets can be shared by two maps acting on the same space. A similar question stands for invariant measures. A particular interesting case…