Related papers: GH-stability and Spectral Decomposition for Group …
Some basic notions and results in Topological Dynamics are extended to continuous groupoid actions in topological spaces. We focus mainly on recurrence properties. Besides results that are analogous to the classical case of group actions,…
We give an overview of how to construct continued fractions on the Heisenberg group $\mathbb{H}$, the projective and planar Siegel models of the group, and how to perform computations on the group using matrices. We discuss and work with…
We study the variety of actions of a fixed (Chevalley) group on arbitrary geodesic, Gromov hyperbolic spaces. In high rank we obtain a complete classification. In rank one, we obtain some partial results and give a conjectural picture.
We generalize the notion of isoperimetric profiles of finitely generated groups to their actions by measuring the boundary of finite subgraphings of the orbit graphing. We prove that like the classical isoperimetric profiles for groups,…
In this note we investigate the two notions of expansivity and strong structural stability for composition operators on $L^p$ spaces, $1 \leq p < \infty$. Necessary and sufficient conditions for such operators to be expansive are provided,…
We study the spectral action approach to higher derivative gravity. The work focuses on the classical aspects. We derive the complete and simplified form of the purely gravitational action up to the 6-derivative terms. We also derive the…
We find sufficient conditions for commutative non-autonomous systems on certain metric spaces to be topologically stable. In particular, we prove that (i) Every mean equicontinuous, mean expansive system with strong average shadowing…
In this paper, we introduce the notions of motivic representation stability that is an algebraic counterpart of the notion of representation stability. In the process, we also introduce the notion of motivic decomposition for varieties…
A group $G$ is said to have property (PH') if there exist finitely many hyperbolic spaces $X_1,\cdots,X_n$ on which $G$ acts coboundedly such that the diagonal action of $G$ on the product $\prod_{i=1}^nX_i$ equipped with $\ell^1$-metric is…
This Part establishes the geometric theory of uniformly hyperbolic sets with explicit quantitative bounds throughout, and contains five main theorems. The Stable Manifold Theorem is proved via the backward graph transform, with a complete…
This paper discusses `geometric property (T)'. This is a property of metric spaces introduced in earlier work of the authors for its applications to K-theory. Geometric property (T) is a strong form of `expansion property': in particular…
We show that an ergodic measure preserving action $\Gamma \curvearrowright (X,\mu)$ of a discrete group $\Gamma$ on a $\sigma$-finite measure space $(X,\mu)$ satisfies the local spectral gap property (introduced by Boutonnet, Ioana and…
We use Lyapunov type functions to give new conditions under which a homeomorphism of a compact metric space has the shadowing property. These conditions are applied to establish the topological stability of some homeomorphisms with…
Recent cosmological observations, including DESI Data Release 2 (DR2) \cite{DESIDR2}, allow for mild redshift evolution of the dark energy equation of state (EoS), motivating renewed interest in the phantom regime ($w<-1$). A no-go result…
This paper deals with the analytic continuation of holomorphic automorphic forms on a Lie group $G$. We prove that for any discrete subgroup $\Gamma$ of $G$ there always exists a non-trivial holomorphic automorphic form, i.e., there exists…
We study linear actions of algebraic groups on smooth projective varieties X. A guiding goal for us is to understand the cohomology of "quotients" under such actions, by generalizing (from reductive to non-reductive group actions) existing…
Motivated by three recent open questions in the study of linear dynamics, we study weighted shifts on sequence spaces. First, we provide an example of a weighted shift on a locally convex space whose topology is generated by a sequence of…
We examine certain phenomena in $C^1$-dynamics from a viewpoint of shadowing and improve a known result on hyperbolic sets. We also review a result on the stability of attractor boundaries from the same viewpoint and derive several…
This paper studies the locally uniform exponential growth and product set growth for a finitely generated group $G$ acting properly on a finite product of hyperbolic spaces. Under the assumption of coarsely dense orbits or shadowing…
We study profinite actions of residually finite groups in terms of weak containment. We show that two strongly ergodic profinite actions of a group are weakly equivalent if and only if they are isomorphic. This allows us to construct…