Related papers: Morphisms of Groupoid Actions and Recurrence

In some particular cases we give criteria for morphic sequences to be almost periodic (=uniformly recurrent). Namely, we deal with fixed points of non-erasing morphisms and with automatic sequences. In both cases a polynomial-time algorithm…

We give a characterization of groups with twisted p-periodic cohomology in terms of group actions on mod p homology spheres. An equivalent algebraic characterization of such groups is also presented.

We extend the notions of nonautonomous dynamics to arbitrary groups, through groupoid morphisms. This also presents a generalization of classic dynamical systems and group actions. We introduce the structure of cotranslations, as a specific…

We study the topological and ergodic dynamics of Bohr almost periodic motions of a topological abelian semigroup acting continuously on a compact metric space.

In this paper we prove some results on the covering morphisms of internal groupoids. We also give a result on the coverings of the crossed modules of groups with operations.

Two types of recurrence sets are introduced for inverse semigroup partial actions in topological spaces. We explore their connections with similar notions for related types of imperfect symmetries (prefix inverse semigroup expansions,…

In this paper, we introduce topological pressure for continuous actions of countable sofic groups on compact metrizable spaces. This generalizes the classical topological pressure for continuous actions of countable amenable groups on such…

We propose categories of $1$-dimensional and multi-dimensional quantum walks. In the categories, an object is a quantum walk, and a morphism is an intertwining operator between two quantum walks. The new framework enables us to discuss…

A Lie groupoid can be thought of as a generalization of a Lie group in which the multiplication is only defined for certain pairs of elements. From another perspective, Lie groupoids can be regarded as manifolds endowed with a type of…

For any $C\in[0,\infty]$ a compact group automorphism $T:X\to X$ is constructed with the property that $$ \frac{1}{n}\log|\{x\in X\mid T^n(x)=x\}|\longrightarrow C. $$ This may be interpreted as a combinatorial analogue of the (still open)…

Recurrence is a fundamental characteristic of dynamical systems with complicated behavior. Understanding the inner structure of recurrence is challenging, especially if the system has many degrees of freedom and is subject to noise. We…

We establish obstructions for groups to act by homeomorphisms on dendrites. For instance, lattices in higher rank simple Lie groups will always fix a point or a pair. The same holds for irreducible lattices in products of connected groups.…

This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…

We consider the category of partial actions, where the group and the set upon which the group acts can vary. Within this framework, we develop a theory of quotient partial actions and prove that this category is both (co)complete and…

In this note we survey recent results on automorphisms of affine algebraic varieties, infinitely transitive group actions and flexibility. We present related constructions and examples, and discuss geometric applications and open problems.

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…

We establish the deformation theory of Lie groupoid morphisms, describe the corresponding deformation cohomology of morphisms, and show the properties of the cohomology. We prove its invariance under isomorphisms of morphisms. Additionally,…

We introduce an abstract topos-theoretic framework for building Galois-type theories in a variety of different mathematical contexts; such theories are obtained from representations of certain atomic two-valued toposes as toposes of…

We introduce the notion of self-similar actions of grouopids on other groupoids and Fell bundles. This leads to a new imprimitivity theorem arising from such dynamics, generalizing many earlier imprimitivity theorems involving group and…

For a path connected, locally path connected and semilocally simply connected space $X$, let $\Pi_1(X)$ denote its topologised fundamental groupoid as established in the first article of this series. Let $\mathcal{E}$ be the category of…