Zobrazeno 1 - 10
of 32
pro vyhledávání: '"Gröger, Maik"'
It is known that if each point $x$ of a dynamical system is generic for some invariant measure $\mu_x$, then there is a strong connection between certain ergodic and topological properties of that system. In particular, if the acting group is abelian
Externí odkaz:
http://arxiv.org/abs/2303.17191
Publikováno v:
Trans. Am. Math. Soc. 376:2395-2418 (2023)
In this article, we define amorphic complexity for actions of locally compact $\sigma$-compact amenable groups on compact metric spaces. Amorphic complexity, originally introduced for $\mathbb Z$-actions, is a topological invariant which measures the
Externí odkaz:
http://arxiv.org/abs/2101.05034
Autor:
Gröger, Maik, Lukina, Olga
We consider a minimal equicontinuous action of a finitely generated group $G$ on a Cantor set $X$ with invariant probability measure $\mu$, and stabilizers of points for such an action. We give sufficient conditions under which there exists a subgrou
Externí odkaz:
http://arxiv.org/abs/1911.00680
Publikováno v:
Nonlinearity 35, pp. 1093-1118, 2022
We develop a new thermodynamic formalism to investigate the transient behaviour of maps on the real line which are skew-periodic $\mathbb{Z}$-extensions of expanding interval maps. Our main focus lies in the dimensional analysis of the recurrent and
Externí odkaz:
http://arxiv.org/abs/1905.09077
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 small changes of their position. By assuming a global perspective and focu
Externí odkaz:
http://arxiv.org/abs/1903.05172
Autor:
Fuhrmann, Gabriel, Gröger, Maik
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. More precisely, we establish a dimensional characterization of the topolo
Externí odkaz:
http://arxiv.org/abs/1812.10789
We study mean equicontinuous actions of locally compact $\sigma$-compact amenable groups on compact metric spaces. In this setting, we establish the equivalence of mean equicontinuity and topo-isomorphy to the maximal equicontinuous factor and provid
Externí odkaz:
http://arxiv.org/abs/1812.10219
We study fractal properties of invariant graphs of hyperbolic and partially hyperbolic skew product diffeomorphisms in dimension three. We describe the critical (either Lipschitz or at all scales H\"older continuous) regularity of such graphs. We pro
Externí odkaz:
http://arxiv.org/abs/1702.06416
Publikováno v:
Ergodic Theory and Dynamical Systems. (2018), 1-35
Given an $\alpha > 1$ and a $\theta$ with unbounded continued fraction entries, we characterise new relations between Sturmian subshifts with slope $\theta$ with respect to (i) an $\alpha$-H\"oder regularity condition of a spectral metric, (ii) level
Externí odkaz:
http://arxiv.org/abs/1601.06435
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 interpreting the attractors as limit objects of the iterates of a continu
Externí odkaz:
http://arxiv.org/abs/1412.6054