ON SOME STATISTICAL PROPERTIES OF DYNAMICAL SYSTEMS

1961 ◽  
pp. 315-320 ◽  
Author(s):  
S. M. Ulam
Keyword(s):  
Dynamical Systems ◽  
Statistical Properties

Statistical properties of turbulent dynamical systems

1999 ◽  
Vol 263 (1-4) ◽  
pp. 155-157 ◽  
Author(s):  
T. Bohr ◽  
M.H. Jensen ◽  
J. Rolf
Keyword(s):  
Dynamical Systems ◽  
Statistical Properties

New developments in the ergodic theory of nonlinear dynamical systems

1994 ◽  
Vol 346 (1679) ◽  
pp. 145-157 ◽  
Keyword(s):  
Dynamical Systems ◽  
Ergodic Theory ◽  
Nonlinear Dynamical Systems ◽  
Statistical Properties ◽  
Strange Attractors ◽  
New Developments ◽  
Nonlinear Dynamical ◽  
Henon Maps ◽  
Open Questions ◽  
Hyperbolic Dynamical Systems

The purpose of this paper is to give a survey of recent results on non-uniformly hyperbolic dynamical systems. The emphasis is on the existence of strange attractors and Sinai-Ruelle-Bowen measures for Henon maps, but we also describe results about statistical properties of such dynamical systems and state some of the open questions in this area.

scholarly journals Intermittent quasistatic dynamical systems: weak convergence of fluctuations

2018 ◽  
Vol 5 (1) ◽  
pp. 8-34 ◽  
Author(s):  
Juho Leppänen
Keyword(s):  
Dynamical Systems ◽  
Weak Convergence ◽  
Time Evolution ◽  
Martingale Problem ◽  
Statistical Properties ◽  
Time Dependent ◽  
Stochastic Diffusion ◽  
Interval Maps ◽  
Well Posed ◽  
Over Time

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.

scholarly journals Inducing schemes for multi-dimensional piecewise expanding maps

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Peyman Eslami
Keyword(s):  
Dynamical Systems ◽  
Statistical Properties ◽  
Expanding Maps ◽  
Return Times ◽  
Return Map ◽  
Exponential Tails ◽  
Inducing Schemes ◽  
Piecewise Expanding Maps

<p style='text-indent:20px;'>We construct inducing schemes for general multi-dimensional piecewise expanding maps where the base transformation is Gibbs-Markov and the return times have exponential tails. Such structures are a crucial tool in proving statistical properties of dynamical systems with some hyperbolicity. As an application we check the conditions for the first return map of a class of multi-dimensional non-Markov, non-conformal intermittent maps.</p>

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