18 citations · 36 across the 12 of their papers we have counts for
16 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…
On the probability of positive finite-time Lyapunov exponents on strange non-chaotic attractors
Flavia Remo, Gabriel Fuhrmann, Tobias Jäger
We study strange non-chaotic attractors in a class of quasiperiodically forced monotone interval maps known as pinched skew products. We prove that the probability of positive time…
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 $…
Tame or wild Toeplitz shifts
Gabriel Fuhrmann, Johannes Kellendonk, Reem Yassawi
We investigate tameness of Toeplitz shifts. By introducing the notion of extended Bratteli-Vershik diagrams, we show that such shifts with finite Toeplitz rank are tame if and only…
On the effect of forcing of fold bifurcations and early-warning signals in population dynamics
Flavia Remo, Gabriel Fuhrmann, Tobias Jäger
The classical fold bifurcation is a paradigmatic example of a critical transition. It has been used in a variety of contexts, including in particular ecology and climate science, t…
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…
On tameness of almost automorphic dynamical systems for general groups
Gabriel Fuhrmann, Dominik Kwietniak
Let be a minimal equicontinuous dynamical system, where is a compact metric space and some topological group acting on . Under very mild assumptions, we show tha…
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…
Irregular model sets and tame dynamics
Gabriel Fuhrmann, Eli Glasner, Tobias Jäger +1
We study the dynamical properties of irregular model sets and show that the translation action on their hull always admits an infinite independence set. The dynamics can therefore…
Rectifiability of a class of invariant measures with one non-vanishing Lyapunov exponent
Gabriel Fuhrmann, Jing Wang
We study order-preserving C^1-circle diffeomorphisms driven by irrational rotations with a Diophantine rotation number. We show that there is a non-empty open set of one-parameter…
Non-smooth saddle-node bifurcations III: strange attractors in continuous time
Gabriel Fuhrmann
Non-smooth saddle-node bifurcations give rise to minimal sets of interesting geometry built of so-called strange non-chaotic attractors. We show that certain families of quasiperio…
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…
Non-Smooth Saddle-Node Bifurcations of Forced Monotone Interval Maps I: Existence of an SNA
Gabriel Fuhrmann
We study one-parameter families of quasi-periodically forced monotone interval maps and provide sufficient conditions for the existence of a parameter at which the respective syste…