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Related papers: Poincar\'e recurrence for observations

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We present a Lohner-type algorithm for rigorous integration of systems of Delay Differential Equations (DDEs) with multiple delays and its application in computation of Poincar\'e maps to study the dynamics of some bounded, eternal…

Dynamical Systems · Mathematics 2024-07-26 Robert Szczelina , Piotr Zgliczyński

In this paper, we study the Hausdorff dimension of self-similar measures and sets on the real line, where the generating iterated function system consists of some maps that share the same fixed point. In particular, we will show that out of…

Dynamical Systems · Mathematics 2025-07-09 Balázs Bárány , Manuj Verma

We introduce a spectrum of monotone coarse invariants for metric measure spaces called Poincar\'{e} profiles. The two extremes of this spectrum determine the growth of the space, and the separation profile as defined by…

Group Theory · Mathematics 2020-11-09 David Hume , John M. Mackay , Romain Tessera

We consider measures supported on the bi-circle and review the recurrence relations satisfied by the orthogonal polynomials associated with these measures constructed using the lexicographical or reverse lexicographical ordering. New…

Classical Analysis and ODEs · Mathematics 2011-02-07 Jeffrey S. Geronimo , Philip Benge

We deal with the inverse problem of reconstructing acoustic material properties or/and external sources for the time-domain acoustic wave model. The traditional measurements consist of repeated active (or passive) interrogations, as the…

Analysis of PDEs · Mathematics 2025-07-15 Soumen Senapati , Mourad Sini

This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…

Dynamical Systems · Mathematics 2022-06-10 Giovanni Russo , Fabian Wirth

We study the variances of the coordinates of an event considered as quantum observables in a Poincare' covariant theory. The starting point is their description in terms of a covariant positive-operator-valued measure on the Minkowski…

Quantum Physics · Physics 2016-09-08 M. Toller

In this paper, I have proved that for a class of polynomial differential systems of degree n+1 ( where n is an arbitrary positive integer) the composition conjecture is true. I give the sufficient and necessary conditions for these…

Classical Analysis and ODEs · Mathematics 2019-05-01 Zhengxin Zhou

Systems of orthogonal polynomials whose recurrence coefficients tend to infinity are considered. A summability condition is imposed on the coefficients and the consequences for the measure of orthogonality are discussed. Also discussed are…

Classical Analysis and ODEs · Mathematics 2014-08-28 A. I. Aptekarev , J. S. Geronimo

It is shown that in transient chaos there is no direct relation between averages in a continuos time dynamical system (flow) and averages using the analogous discrete system defined by the corresponding Poincare map. In contrast to…

Chaotic Dynamics · Physics 2009-11-07 Z. Kaufmann , H. Lustfeld

We prove that Poisson measures are invariant under (random) intensity preserving transformations whose finite difference gradient satisfies a cyclic vanishing condition. The proof relies on moment identities of independent interest for…

Probability · Mathematics 2011-02-24 Nicolas Privault

Invertible compositions of one-dimensional maps are studied which are assumed to include maps with non-positive Schwarzian derivative and others whose sum of distortions is bounded. If the assumptions of the Koebe principle hold, we show…

Dynamical Systems · Mathematics 2016-09-06 Grzegorz Swiatek

We explore the problem of finding the Hausdorff dimension of the set of points that recur to shrinking targets on a self-affine fractal. To be exact, we study the dimension of a certain related symbolic recurrence set. In many cases this…

Dynamical Systems · Mathematics 2018-12-19 Henna Koivusalo , Felipe A. Ramírez

This paper proves an equality in law between the invariant measure of a reflected system of Brownian motions and a vector of point-to-line last passage percolation times in a discrete random environment. A consequence describes the…

Probability · Mathematics 2019-07-17 Will FitzGerald , Jon Warren

Over the last decade it has become clear that discrete Painlev\'e equations appear in a wide range of important mathematical and physical problems. Thus, the question of recognizing a given non-autonomous recurrence as a discrete Painlev\'e…

Exactly Solvable and Integrable Systems · Physics 2020-12-30 Anton Dzhamay , Galina Filipuk , Alexander Stokes

We consider elliptic diffusion processes on $\mathbb R^d$. Assuming that the drift contracts distances outside a compact set, we prove that, at a sufficiently high temperature, the Markov semi-group associated to the process is a…

Probability · Mathematics 2023-07-20 Pierre Monmarché

In this paper we study the asymptotic behavior of nonoscillatory solutions for high order differential equations of Poincar\'e type. We introduce two new and more weak than classical hypotheses on the coefficients, which implies a well…

Classical Analysis and ODEs · Mathematics 2018-05-15 Aníbal Coronel , Fernando Huancas

In this paper we present a general scheme for how to relate differential equations for the recurrence coefficients of semi-classical orthogonal polynomials to the Painlev\'e equations using the geometric framework of the Okamoto Space of…

Classical Analysis and ODEs · Mathematics 2021-12-08 Anton Dzhamay , Galina Filipuk , Alexander Stokes

In this paper we characterize the mixing properties in the advection of passive tracers by exploiting the extreme value theory for dynamical systems. With respect to classical techniques directly related to the Poincar\'e recurrences…

Chaotic Dynamics · Physics 2014-05-07 Davide Faranda , Xavier Leoncini , Sandro Vaienti

We consider invariant measures of maps on manifolds whose correlations decay at a sufficient rate and which satisfy a geometric contraction property. We then prove the that the limiting distribution of returns to geometric balls is…

Dynamical Systems · Mathematics 2016-02-08 Nicolai Haydn , Fan Yang