Related papers: Definable Topological Dynamics of $SL_2(\mathbb{C}…

In this paper we study groups definable in existentially closed partial differential fields of characteristic 0 with an automorphism which commutes with the derivations. In particular, we study Zariski dense definable subgroups of simple…

We characterize amenability of subspaces of $C(S)$, where $S$ is a semitopological semigroup, in terms of fixed point properties of nonexpansive actions. In particular, we give a complete characterization of a semitopological semigroup with…

Conformable derivatives provide a fractional-looking calculus that remains local and admits a simple representation through classical derivatives with explicit weights. In this paper we develop a systematic operator-theoretic perspective…

We endow a topological group $(G, \tau)$ with a coarse structure defined by the smallest group ideal $S_{\tau} $ on $G$ containing all converging sequences with their limits and denote the obtained coarse group by $(G, S_{\tau})$. If $G$ is…

This is a survey of the recent development of the study of topological full groups of etale groupoids on the Cantor set. Etale groupoids arise from dynamical systems, e.g. actions of countable discrete groups, equivalence relations. Minimal…

The outlines of a "Galois theory" for bimeromorphic geometry is here developed, via the study of model-theoretic definable binding groups in the theory CCM of compact complex spaces. As an application, a structure theorem about principal…

For each countable residually finite group $G$, we present examples of irregular Toeplitz subshifts in $\{0,1\}^G$ that are topo-isomorphic extensions of its maximal equicontinuous factor. To achieve this, we first establish sufficient…

Motivated by Gromov's geodesic flow problem on hyperbolic groups $G$, we develop in this paper an analog using random walks. This leads to a notion of a harmonic analog $\Theta$ of the Bowen-Margulis-Sullivan measure on $\partial^2 G$. We…

Consider the algebraic dynamics on a torus T=G_m^n given by a matrix M in GL_n(Z). Assume that the characteristic polynomial of M is prime to all polynomials X^m-1. We show that any finite equivariant map from another algebraic dynamics…

To any automorphism, $\alpha$, of a totally disconnected, locally compact group, $G$, there is associated a compact, $\alpha$-stable subgroup of $G$, here called the \emph{nub} of $\alpha$, on which the action of $\alpha$ is topologically…

We develop the theory of ultracoproducts and weak containment for flows of arbitrary topological groups. This provides a nice complement to corresponding theories for p.m.p. actions and unitary representations of locally compact groups. For…

We study idempotent measures and the structure of the convolution semigroups of measures over definable groups. We isolate the property of generic transitivity and demonstrate that it is sufficient (and necessary) to develop stable group…

Newton flows are dynamical systems generated by a continuous, desingularized Newton method for mappings from a Euclidean space to itself. We focus on the special case of meromorphic functions on the complex plane. Inspired by the analogy…

We use ideas from topological dynamics (amenability), combinatorics (structural Ramsey theory) and model theory (Fra\" {i}ss\' e limits) to study closed amenable subgroups $G$ of the symmetric group $S_\infty$ of a countable set, where…

We define a semidirect product groupoid of a system of partially defined local homeomorphisms $T=(T_{1},..., T_{r})$. We prove that this construction gives rise to amenable groupoids. The associated algebra is a Cuntz-like algebra. We use…

We discuss the topology of the symmetry groups appearing in compactified (super-)gravity, and discuss two applications. First, we demonstrate that for 3 dimensional sigma models on a symmetric space G/H with G non-compact and H the maximal…

We introduce the notion of finite slope families to encode the local properties of the p-adic families of Galois representations appearing in the work of Harris, Lan, Taylor and Thorne on the construction of Galois representations for…

The motivation for this paper is to extend the known model theoretic treatment of differential Galois theory to the case of linear difference equations (where the derivative is replaced by an automorphism.) The model theoretic difficulties…

We continue in this paper the study of locally minimal groups started in \cite{LocMin}. The minimality criterion for dense subgroups of compact groups is extended to local minimality. Using this criterion we characterize the compact abelian…

Conformable derivatives involve a fractional parameter while preserving locality: on smooth functions they reduce to a classical derivative multiplied by an explicit weight. Exploiting this structural feature, we show that conformable time…