Related papers: Scaling entropy growth gap

We study the growth of typical groups from the family of $p$-groups of intermediate growth constructed by the second author. We find that, in the sense of category, a generic group exhibits oscillating growth with no universal upper bound.…

We prove a general version of the amenability conjecture in the unified setting of a Gromov hyperbolic group G acting properly cocompactly either on its Cayley graph, or on a CAT(-1)-space. Namely, for any subgroup H of G, we show that H is…

Let $M$ be a compact surface with boundary. We are interested in the question of how a group action on $M$ permutes a finite invariant set $X \subset int(M)$. More precisely, how the algebraic properties of the induced group of permutations…

Let $G,H$ be two countable amenable groups. We introduce the notion of group charts, which gives us a tool to embed an arbitrary $H$-subshift into a $G$-subshift. Using an entropy addition formula derived from this formalism we prove that…

In the current paper we attempt to transfer the notion of the projectional entropy, originally defined for multidimensional subshifts, to the case of actions of amenable groups. The main theorem states that if a system is strongly…

A variety of behaviors of entropy functions of random walks on finitely generated groups is presented, showing that for any $\frac{1}{2}\leq \alpha\leq\beta\leq1$, there is a group $\Gamma$ with measure $\mu$ equidistributed on a finite…

It is shown that each discrete countable infinite amenable group admits a 0-entropy mixing action on a standard probability space.

The group of automorphisms of a symbolic dynamical system is countable, but often very large. For example, for a mixing subshift of finite type, the automorphism group contains isomorphic copies of the free group on two generators and the…

Let Mod(S) denote the mapping class group of a compact, orientable surface S. We prove that finitely generated subgroups of Mod(S) which are not virtually abelian have uniform exponential growth with minimal growth rate bounded below by a…

Extensive amenability is a property of group actions which has recently been used as a tool to prove amenability of groups. We study this property and prove that it is preserved under a very general construction of semidirect products. As…

The goal of this article is to study results and examples concerning finitely presented covers of finitely generated amenable groups. We collect examples of groups $G$ with the following properties: (i) $G$ is finitely generated, (ii) $G$…

We say that two free probability-measure-preserving actions of countable groups are Shannon orbit equivalent if there is an orbit equivalence between them whose associated cocycle partitions have finite Shannon entropy. We show that if the…

A probability measure preserving action of a discrete amenable group $G$ is said to be dominant if it is isomorphic to a generic extension of itself. Recently, it was shown that for $G = \mathbb{Z}$, an action is dominant if and only if it…

Let $\Gamma $ be an infinite discrete group and $\mathsf{A}\subset \Gamma $ a nonempty finite subset. The set of permutations $\sigma $ of $\Gamma $ such that $s^{-1}\sigma (s)\in \mathsf{A}$ for every $s\in \Gamma $ can be identified with…

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,…

Symbolic Extension Entropy Theorem (SEET) describes the possibility of a lossless digitalization of a dynamical system by extending it to a subshift. It gives an estimate on the entropy of symbolic extensions (and the necessary number of…

Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a…

We consider an entropy-type invariant which measures the polynomial volume growth of submanifolds under the iterates of a map, and we establish sharp uniform lower bounds of this invariant for the following classes of symplectomorphisms of…

Measure-theoretic and topological entropy are classical invariants in the theory of dynamical systems. There are several recently developed entropy type invariants for systems of sub-exponential growth: sequence entropy, slow entropy,…

In this short note, for countably infinite amenable group actions, we provide topological proofs for the following results: Bowen topological entropy (dimensional entropy) of the whole space equals the usual topological entropy along…