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We study a generalized notion of a homogeneous skew-product extension of a probability-preserving system in which the homogeneous space fibres are allowed to vary over the ergodic decomposition of the base. The construction of such…

Dynamical Systems · Mathematics 2009-11-11 Tim Austin

We use a Poisson point process approach to prove distributional convergence to a stable law for non square-integrable observables $\phi: [0,1]\to R$, mostly of the form $\phi (x) = d(x,x_0)^{-\frac{1}{\alpha}}$,$0<\alpha\le 2$, on…

Dynamical Systems · Mathematics 2024-07-24 An Chen , Matthew Nicol , Andrew Török

In this paper, we establish a variational principle, between the fiber Bowen's topological entropy on conditional level sets of Birkhoff average and fiber measure-theoretical entropy, for the skew product transformation driven by a uniquely…

Dynamical Systems · Mathematics 2024-06-26 Nian Liu , Xue Liu

We prove a new result in the area of hitting time statistics. Currently, there is a lot of papers showing that the first entry times into cylinders or balls are often faster than the Birkhoff's Ergodic Theorem would suggest. We provide an…

Dynamical Systems · Mathematics 2019-08-02 Łukasz Pawelec , Mariusz Urbański

We consider the inverse problem of finding unknown elastic parameters from internal measurements of displacement fields for tissues. The measurements are made on the entirety of a smooth domain. Since tissues can be modeled as…

Analysis of PDEs · Mathematics 2014-09-19 Habib Ammari , Alden Waters , Hai Zhang

We compare ergodic properties of the kinetic energy for three stochastic models of subrecoil-laser-cooled gases. One model is based on a heterogeneous random walk (HRW), another is an HRW with long-range jumps (the exponential model), and…

Statistical Mechanics · Physics 2022-07-13 Takuma Akimoto , Eli Barkai , Günter Radons

Linear stability of inviscid, parallel, and stably stratified shear flow is studied under the assumption of smooth strictly monotonic profiles of shear flow and density, so that the local Richardson number is positive everywhere. The…

Fluid Dynamics · Physics 2016-05-04 Makoto Hirota , Philip J. Morrison

We obtain central limit theorem, local limit theorems and renewal theorems for stationary processes generated by skew product maps $T(\om,x)=(\te\om,T_\om x)$ together with a $T$-invariant measure, whose base map $\te$ satisfies certain…

Probability · Mathematics 2020-12-02 Yeor Hafouta

We study an intermittent map which has exactly two ergodic invariant densities. The densities are supported on two subintervals with a common boundary point. Due to certain perturbations, leakage of mass through subsets, called holes, of…

Dynamical Systems · Mathematics 2015-05-28 Wael Bahsoun , Sandro Vaienti

Reservoir computing systems are constructed using a driven dynamical system in which external inputs can alter the evolving states of a system. These paradigms are used in information processing, machine learning, and computation. A…

Neural and Evolutionary Computing · Computer Science 2023-04-26 G Manjunath , Juan-Pablo Ortega

Turbulence in wall-bounded flows is characterized by stable statistics. Although, in many turbulent systems, this stable statistical state corresponds to a stable fixed point of an associated statistical state dynamics (SSD) closed at…

Fluid Dynamics · Physics 2023-12-14 Brian F. Farrell , Petros J. Ioannou

This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…

Probability · Mathematics 2019-05-02 Adrian N. Bishop , Pierre Del Moral

The authors consider stochastic aspects of the stabilization problem for two and three-dimensional Oseen equations with help of feedback control defined on a part of the fluid boundary. Stochastic issues arise when inevitable unpredictable…

Analysis of PDEs · Mathematics 2007-05-23 Jinqiao Duan , Andrei V. Fursikov

In this paper we study decay of correlations and limit theorems for generalized baker's transformations. Our examples are piecewise non-uniformly hyperbolic maps on the unit square that posses two spatially separated lines of indifferent…

Dynamical Systems · Mathematics 2018-02-07 Seth W. Chart

This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and the initial displacement in a damped biharmonic wave equation. The data consist of the boundary Cauchy data for the Laplacian of…

Analysis of PDEs · Mathematics 2026-05-18 Minghui Bi , Yixian Gao

This paper concerns parameterized convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional Banach (resp. finite-dimensional) spaces and that are indexed by an arbitrary fixed set T…

Optimization and Control · Mathematics 2011-02-07 M. J. CÁnovas , M. A. LÓpez , B. S. Mordukhovich , J. Parra

This work investigates a three-dimensional slow-fast stochastic system with quadratic nonlinearity and additive noise, inspired by fluid dynamics. The deterministic counterpart exhibits a periodic orbit and a slow manifold. We demonstrate…

Dynamical Systems · Mathematics 2025-01-22 Mickaël D. Chekroun , Jeroen S. W. Lamb , Christian J. Pangerl , Martin Rasmussen

This article is devoted to the stability of error bounds (local and global) for semi-infinite convex constraint systems in Banach spaces. We provide primal characterizations of the stability of local and global error bounds when systems are…

Optimization and Control · Mathematics 2023-02-07 Zhou Wei , Michel Théra , Jen-Chih Yao

The aim of the paper is to present various asymptotic behaviors of skew-evolution semiflows in Banach spaces, as exponential decay, instability, exponential in- stability and integral instability. Relations between these asymptotic…

Classical Analysis and ODEs · Mathematics 2008-01-23 Codruţa Stoica

This paper establishes the quantitative stability of invariant measures $\mu_{\alpha}$ for $\mathbb{R}^d$-valued ergodic stochastic differential equations driven by rotationally invariant multiplicative $\alpha$-stable processes with…

Probability · Mathematics 2025-09-17 Xinghu Jin , Xiaolong Zhang