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Related papers: Fuglede-Kadison Determinants and Sofic Entropy

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We show that many algebraic actions of higher-rank abelian groups on zero-dimensional groups are mutually disjoint. The proofs exploit differences in the entropy geometry arising from subdynamics and a form of Abramov--Rokhlin formula for…

Dynamical Systems · Mathematics 2007-05-23 Manfred Einsiedler , Thomas Ward

We discuss the finiteness of the topological entropy of continuous endomorphims for some classes of locally compact groups. Firstly, we focus on the abelian case, imposing the condition of being compactly generated, and note an interesting…

Group Theory · Mathematics 2024-03-01 Francesco G. Russo , Olwethu Waka

For a locally compact sofic group continuously acting on a compact metric space, we first study the relative sofic entropy and prove an additive inequality relating sofic entropy and relative sofic entropy. Moreover, it is shown that the…

Dynamical Systems · Mathematics 2025-11-25 Xianqiang Li , Zhuowei Liu

In 1965 Adler, Konheim and McAndrew defined the topological entropy for continuous self-maps of compact spaces. Topological entropy is very well-understood for endomorphisms of compact Abelian groups. A fundamental result in this context is…

Group Theory · Mathematics 2013-02-20 Anna Giordano Bruno , Simone Virili

Let X be a normal affine T-variety of complexity at most one over a perfect field k, where T stands for the split algebraic torus. Our main result is a classification of additive group actions on X that are normalized by the T-action. This…

Algebraic Geometry · Mathematics 2016-01-28 Kevin Langlois , Alvaro Liendo

We prove that if a free ergodic action of a countably infinite group has positive Rokhlin entropy (or, less generally, positive sofic entropy) then it factors onto all Bernoulli shifts of lesser or equal entropy. This extends to all…

Dynamical Systems · Mathematics 2019-05-23 Brandon Seward

We study Tonelli Lagrangian systems on the 2-torus in energy levels above Ma\~n\'e's strict critical value and analyize the structure of global minimizers in the spirit of Morse, Hedlund and Bangert. In the case where the topological…

Dynamical Systems · Mathematics 2013-08-30 Jan Philipp Schröder

We give an infinitesimal criterion, in the analytic setting, for a vector space to be locally homogeneous under some group action. Our approach differs from those which resort to an inverse function theorem (e.g. those of Moser, Zehnder or…

Dynamical Systems · Mathematics 2011-10-12 Jacques Féjoz , Mauricio Garay

We study an invariant of dynamical systems called naive entropy, which is defined for both measurable and topological actions of any countable group. We focus on nonamenable groups, in which case the invariant is two-valued, with every…

Dynamical Systems · Mathematics 2016-02-23 Peter Burton

In the following text we show set--theoretical entropy of Euler's totient function and contravariant set--theoretical entropy of Dedekind psi function are zero. Also contravariant set--theoretical entropy of Euler's totient function and…

Number Theory · Mathematics 2024-01-19 Fatemah Ayatollah Zadeh Shirazi , Reza Yaghmaeian

We consider quantum algebras of observables associated with subregions in theories of Einstein gravity coupled to matter in the $G_N\rightarrow 0$ limit. When the subregion is spatially compact or encompasses an asymptotic boundary, we…

High Energy Physics - Theory · Physics 2024-02-07 Kristan Jensen , Jonathan Sorce , Antony Speranza

We generalize Bourgain-Lindenstrauss-Michel-Venkatesh's recent one-dimensional quantitative density result to abelian algebraic actions on higher dimensional tori. Up to finite index, the group actions that we study are conjugate to the…

Dynamical Systems · Mathematics 2010-04-02 Zhiren Wang

We give algebraic characterizations for expansiveness of algebraic actions of countable groups. The notion of p-expansiveness is introduced for algebraic actions, and we show that for countable amenable groups, a finitely presented…

Dynamical Systems · Mathematics 2014-04-17 Nhan-Phu Chung , Hanfeng Li

Ergodic and combinatorial results obtained in [10] involved measure preserving actions of the affine group ${\mathcal A}_K$ of a countable field $K$. In this paper we develop a new approach based on ultrafilter limits which allows one to…

Dynamical Systems · Mathematics 2015-09-28 Vitaly Bergelson , Joel Moreira

In \cite{BK02}, M. Bonk and B. Kleiner proved a rigidity theorem for expanding quasi-M\"obius group actions on Ahlfors $n$-regular metric spaces with topological dimension $n$. This led naturally to a rigidity result for quasi-convex…

Metric Geometry · Mathematics 2016-01-19 Kyle Kinneberg

Dan Rudolph showed that for an amenable group $\Gamma$, the generic measure-preserving action of $\Gamma$ on a Lebesgue space has zero entropy. Here this is extended to nonamenable groups. In fact, the proof shows that every action is a…

Dynamical Systems · Mathematics 2016-05-20 Lewis Bowen

Let $\Gamma$ be a sofic group with a copy of $\mathbb{Z}$ in its center. We construct an uncountable family of pairwise nonisomorphic measure-preserving $\Gamma$ actions with completely positive entropy, none of which is a factor of a…

Dynamical Systems · Mathematics 2016-04-04 Peter Burton

We introduce the algebraic entropy for endomorphisms of arbitrary abelian groups, appropriately modifying existing notions of entropy. The basic properties of the algebraic entropy are given, as well as various examples. The main result of…

Group Theory · Mathematics 2016-05-04 Dikran Dikranjan , Anna Giordano Bruno

We show that for a finitely generated group of $C^2$ circle diffeomorphisms, the entropy of the action equals the entropy of the restriction of the action to the non-wandering set.

Dynamical Systems · Mathematics 2009-01-29 Eduardo Jorquera

Follow-up comment by the author: Theorem 2.2 in this paper is a special case of Theorems 1.1 and 4.1 in the article "Weighted thermodynamic formalism on subshifts and applications", Asian J. Math. 16 (2012), by J. Barral and D. J. Feng. In…

Dynamical Systems · Mathematics 2024-12-17 Nima Alibabaei
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