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Related papers: Dynamical Borel-Cantelli lemmas for Gibbs measures

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In \cite{D3}, Donaldson defines a dynamical system on the space of Fubini-Study metrics on a polarized compact K\"ahler manifold. Sano proved that if there exists a balanced metric for the polarization, then this dynamical system always…

Differential Geometry · Mathematics 2008-12-06 Reza Seyyedali

A classical question about a metric space is whether Borel measures on the space are determined by their values on balls. We show that for any given measure this property is stable under Gromov-Wasserstein convergence of metric measure…

Algebraic Topology · Mathematics 2024-01-23 Anne van Delft , Andrew J. Blumberg

The strict connection between Lie point-symmetries of a dynamical system and its constants of motion is discussed and emphasized, through old and new results. It is shown in particular how the knowledge of a symmetry of a dynamical system…

Mathematical Physics · Physics 2015-06-16 Giampaolo Cicogna

The purpose of this article is to construct a toolbox, in Dynamical Systems, to support the idea that ``whenever we can prove a limit theorem in the classical sense for a dynamical system, we can prove a suitable almost-sure version based…

Dynamical Systems · Mathematics 2007-05-23 J-R Chazottes , S Gouezel

The Bessel point process is a rigid point process on the positive real line and its conditional measure on a bounded interval $[0,R]$ is almost surely an orthogonal polynomial ensemble. In this article, we show that if $R$ tends to…

Probability · Mathematics 2021-05-14 Leslie Molag , Marco Stevens

In the study of some dynamical systems the limsup set of a sequence of measurable sets is often of interest. The shrinking targets and recurrence are two of the most commonly studied problems that concern limsup sets. However, the zero-one…

Dynamical Systems · Mathematics 2023-02-08 Dmitry Kleinbock , Jiajie Zheng

In this paper we provide examples of topological dynamical systems having either finite or countable scrambled sets. In particular we study conditions for the existence of Li-Yorke, asymptotic and distal pairs in constant--length…

Dynamical Systems · Mathematics 2009-11-13 François Blanchard , Fabien Durand , Alejandro Maass

This paper studies limit measures of stationary measures of stochastic ordinary differential equations on the Euclidean space and tries to determine which invariant measures of an unperturbed system will survive. Under the assumption for…

Dynamical Systems · Mathematics 2022-01-28 Tianyuan Xu , Lifeng Chen , Jifa Jiang

We give an explicit description of all finite Borel measures on Noetherian topological spaces X, and characterize them as objects dual to a space of functions on X. We use these results to study the asymptotic behavior of continuous…

Dynamical Systems · Mathematics 2012-12-21 William Gignac

We describe the approximation of a continuous dynamical system on a p. l. manifold or Cantor set by a tractable system. A system is tractable when it has a finite number of chain components and, with respect to a given full background…

Dynamical Systems · Mathematics 2019-06-03 Ethan Akin

We consider stochastic dynamical systems on ${\mathbb{R}}$, that is, random processes defined by $X_n^x=\Psi_n(X_{n-1}^x)$, $X_0^x=x$, where $\Psi _n$ are i.i.d. random continuous transformations of some unbounded closed subset of…

Probability · Mathematics 2015-06-05 Sara Brofferio , Dariusz Buraczewski

The problem of the dynamical stability of anistropic systems is studied, by proposing a criterion in terms of the adiabatic local index $\gamma$. The result has general validity and can be applied to several physical situations.…

General Relativity and Quantum Cosmology · Physics 2019-02-14 Giuseppe Alberti , Marco Merafina

This report investigates the dynamical stability conjectures of Palis and Smale, and Pugh and Shub from the standpoint of numerical observation and lays the foundation for a stability conjecture. As the dimension of a dissipative dynamical…

Chaotic Dynamics · Physics 2007-05-23 D. J. Albers , J. C. Sprott

We examine domain-valued maxitive measures defined on the Borel subsets of a topological space. Several characterizations of regularity of maxitive measures are proved, depending on the structure of the topological space. Since every…

General Topology · Mathematics 2013-02-12 Paul Poncet

We consider a discrete-time temporally-homogeneous conservative Markov process. We show that extremality of reversible measure implies extremality of invariant measure. Using analogue of Dirichlet form, we modify a proof that in stochastic…

General Mathematics · Mathematics 2023-12-25 Hiroki Yagisita

We consider a gas whose each particle is characterised by a pair $(x,v_x)$ with the position $x\in \mathbb R^d$ and the velocity $v_x\in \mathbb R^d_0= \mathbb R^d\setminus \{0\}$. We define Gibbs measures on the cone of vector-valued…

Probability · Mathematics 2025-07-15 Luca Di Persio , Yuri Kondratiev , Viktorya Vardanyan

Let $G$ be a locally compact second countable group equipped with an admissible non-degenerate Borel probability measure $\mu$. We generalize the notion of $\mu$-stationary systems to $\mu$-stationary $G$-factor maps $\pi: (X,\nu)\to…

Dynamical Systems · Mathematics 2024-05-28 Tattwamasi Amrutam , Martin Klötzer , Hanna Oppelmayer

An existing dialogue between number theory and dynamical systems is advanced. A combinatorial device gives necessary and sufficient conditions for a sequence of non-negative integers to count the periodic points in a dynamical system. This…

Number Theory · Mathematics 2007-05-23 Graham Everest , Yash Puri , Thomas Ward

Using Caratheodory measures, we associate to each positive orbit ${\mathcal O}_{f}^{+}(x)$ of a measurable map $f$, a Borel measure $\eta_{x}$. We show that $\eta_{x}$ is $f$-invariant whenever $f$ is continuous or $\eta_{x}$ is a…

Dynamical Systems · Mathematics 2020-12-17 Vitor Araujo , Vilton Pinheiro

We describe a family $\phi_{\lambda}$ of dynamical systems on the unit interval which preserve Bernoulli convolutions. We show that if there are parameter ranges for which these systems are piecewise convex, then the corresponding Bernoulli…

Dynamical Systems · Mathematics 2015-10-28 Tom Kempton , Tomas Persson
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