18 citations · 30 across the 9 of their papers we have counts for
11 papers
Period spectrum and rigidity of interval maps
Gabriel Fuhrmann, Maik Gröger, Alejandro Passeggi
We study the extent to which periodic orbits determine a one-dimensional dynamical system. In particular, we show that they determine every topologically mixing interval map. More…
On the continuity of Følner averages
Gabriel Fuhrmann, Maik Gröger, Till Hauser
It is known that if each point of a dynamical system is generic for some invariant measure , then there is a strong connection between certain ergodic and topological prop…
Amorphic complexity of group actions with applications to quasicrystals
Gabriel Fuhrmann, Maik Gröger, Tobias Jäger +1
In this article, we define amorphic complexity for actions of locally compact -compact amenable groups on compact metric spaces. Amorphic complexity, originally introduced for $…
Thermodynamic formalism for transient dynamics on the real line
Maik Gröger, Johannes Jaerisch, Marc Kesseböhmer
We develop a new thermodynamic formalism to investigate the transient behaviour of maps on the real line which are skew-periodic -extensions of expanding interval maps.…
The bifurcation set as a topological invariant for one-dimensional dynamics
Gabriel Fuhrmann, Maik Gröger, Alejandro Passeggi
For a continuous map on the unit interval or circle, we define the bifurcation set to be the collection of those interval holes whose surviving set is sensitive to arbitrarily smal…
Constant length substitutions, iterated function systems and amorphic complexity
Gabriel Fuhrmann, Maik Gröger
We show how geometric methods from the general theory of fractal dimensions and iterated function systems can be deployed to study symbolic dynamics in the zero entropy regime. Mor…
The structure of mean equicontinuous group actions
Gabriel Fuhrmann, Maik Gröger, Daniel Lenz
We study mean equicontinuous actions of locally compact -compact amenable groups on compact metric spaces. In this setting, we establish the equivalence of mean equicontinuity a…
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…
Amorphic complexity
G. Fuhrmann, M. Gröger, T. Jäger
We introduce amorphic complexity as a new topological invariant that measures the complexity of dynamical systems in the regime of zero entropy. Its main purpose is to detect the v…
Non-smooth saddle-node bifurcations II: dimensions of strange attractors
Gabriel Fuhrmann, Maik Gröger, Tobias Jäger
We study the geometric and topological properties of strange non-chaotic attractors created in non-smooth saddle-node bifurcations of quasiperiodically forced interval maps. By int…
Coupled skinny baker's maps and the Kaplan-Yorke conjecture
Maik Gröger, Brian R. Hunt
The Kaplan-Yorke conjecture states that for "typical" dynamical systems with a physical measure, the information dimension and the Lyapunov dimension coincide. We explore this conj…