Related papers: The Morse minimal system is nearly continuously Ka…

We study amenable minimal Cantor systems of free groups arising from the diagonal actions of the boundary actions and certain Cantor systems. It is shown that every virtually free group admits continuously many amenable minimal Cantor…

Resolving a conjecture of von Neumann, Ogata's theorem in arXiv:1111.5933 showed the highly nontrivial result that arbitrarily many matrices corresponding to macroscopic observables with $N$ sites and a fixed site dimension $d$ are…

For a ${\mathbb Z}^{d}$-topological dynamical system $(X, T, {\mathbb Z}^{d})$, an isomomorphism is a self-homeomorphism $\phi : X\to X$ such that for some matrix $M\in {\rm GL}(d,{\mathbb Z})$ and any ${n}\in {\mathbb Z}^{d}$, $\phi\circ…

For a proper geodesic metric space $X$, the Morse boundary $\partial_*X$ focuses on the hyperbolic-like directions in the space $X$. It is a quasi-isometry invariant. That is, a quasi-isometry between two hyperbolic spaces induces a…

Given a topological dynamical system $(X,T)$ and an arithmetic function $\boldsymbol{u}\colon\mathbb{N}\to\mathbb{C}$, we study the strong MOMO property (relatively to $\boldsymbol{u}$) which is a strong version of…

We derive the Christoffel-Geronimus-Uvarov transformations of a system of bi-orthogonal polynomials and associated functions on the unit circle, that is to say the modification of the system corresponding to a rational modification of the…

We construct a family of shift spaces with almost specification and multiple measures of maximal entropy. This answers a question from Climenhaga and Thompson [Israel J. Math. 192 (2012), no. 2, 785--817]. Elaborating on our examples we…

Each topological group $G$ admits a unique universal minimal dynamical system $(M(G),G)$. When $G$ is a non-compact locally compact group the phase space $M(G)$ of this universal system is non-metrizable. There are however topological…

Several important conjectures in Fractal Geometry can be summarised as follows: If the dimension of a self-similar measure in $\mathbb{R}$ does not equal its expected value, then the underlying iterated function system contains an exact…

We first explain how to endow the space of subequivalence relations of any non-singular countable equivalence relation with a Polish topology, extending the framework of Kechris' recent monograph on subequivalence relations of probability…

Given a flat metric one may generate a local Hamiltonian structure via the fundamental result of Dubrovin and Novikov. More generally, a flat pencil of metrics will generate a local bi-Hamiltonian structure, and with additional…

It has been proved in [J.-D. Hardtke, J. Math. Phys. Anal. Geom. 16, no.2, 119--137 (2020)] that a K\"othe-Bochner space $E(X)$ is locally octahedral/locally almost square if $X$ has the respective property and the simple functions are…

We investigate in this work some situations where it is possible to estimate or determine the upper and the lower $q$-generalized fractal dimensions $D^{\pm}_{\mu}(q)$, $q\in\mathbb{R}$, of invariant measures associated with continuous…

For a given bi-continuous semigroup T on a Banach space X we define its adjoint on an appropriate closed subspace X^o of the norm dual X'. Under some abstract conditions this adjoint semigroup is again bi-continuous with respect to the weak…

Let $\mu$ be a probability measure on $\mathbb{R}^n$ with a bounded density $f$. We prove that the marginals of $f$ on most subspaces are well-bounded. For product measures, studied recently by Rudelson and Vershynin, our results show there…

We show that linear complexity is the threshold for the emergence of Kakutani inequivalence for measurable systems supported on a minimal subshift. In particular, we show that there are minimal subshifts of arbitrarily low super-linear…

A Borel system consists of a measurable automorphism of a standard Borel space. We consider Borel embeddings and isomorphisms between such systems modulo null sets, i.e. sets which have measure zero for every invariant probability measure.…

Let $\Om$ be a Borel subset of $S^\Bbb N$ where $S$ is countable. A measure is called exchangeable on $\Om$, if it is supported on $\Om$ and is invariant under every Borel automorphism of $\Om$ which permutes at most finitely many…

Revisiting the notion of m-almost equicontinuous cellular automata introduced by R. Gilman, we show that the sequence of image measures of a shift ergodic measure m by iterations of a m-almost equicontinuous automata F, converges in Cesaro…

Let $A$ be a compact set in $\Rp$ of Hausdorff dimension $d$. For $s\in(0,d)$, the Riesz $s$-equilibrium measure $\mu^{s,A}$ is the unique Borel probability measure with support in $A$ that minimizes $$…