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Nonautonomous Dynamical Systems

formerly Nonautonomous and Stochastic Dynamical Systems

Editor-in-Chief: Diagana, Toka

Managing Editor: Cánovas, Jose


Mathematical Citation Quotient (MCQ) 2017: 0.71

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Online
ISSN
2353-0626
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Intermittent quasistatic dynamical systems: weak convergence of fluctuations

Juho Leppänen
Published Online: 2018-04-03 | DOI: https://doi.org/10.1515/msds-2018-0002

Abstract

This paper is about statistical properties of quasistatic dynamical systems. These are a class of non-stationary systems that model situations where the dynamics change very slowly over time due to external influences. We focus on the case where the time-evolution is described by intermittent interval maps (Pomeau-Manneville maps) with time-dependent parameters. In a suitable range of parameters, we obtain a description of the statistical properties as a stochastic diffusion, by solving a well-posed martingale problem. The results extend those of a related recent study due to Dobbs and Stenlund, which concerned the case of quasistatic (uniformly) expanding systems.

Keywords: Quasistatic dynamical system; intermittency; Pomeau-Manneville map; weak convergence; martingale problem

MSC 2010: 37C60; 37D25; 37A10; 60G44; 60H10

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About the article

Received: 2017-11-13

Accepted: 2018-02-01

Published Online: 2018-04-03


Citation Information: Nonautonomous Dynamical Systems, Volume 5, Issue 1, Pages 8–34, ISSN (Online) 2353-0626, DOI: https://doi.org/10.1515/msds-2018-0002.

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© 2018. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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