Journal ArticleDOI
A probabilistic approach to intermittency
TLDR
This method essentially gives the optimal polynomial bound for the decay of correlations, the degree depending on the order of the tangency at the neutral fixed point.Abstract:
We present an original approach which allows us to investigate the statistical properties of a non-uniformly hyperbolic map on the interval. Based on a stochastic approximation of the deterministic map, this method essentially gives the optimal polynomial bound for the decay of correlations, the degree depending on the order of the tangency at the neutral fixed point.read more
Citations
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Journal ArticleDOI
Recurrence times and rates of mixing
TL;DR: In this paper, the authors considered the setting of a map making "nice" return to a reference set, and defined criteria for the existence of equilibria, speed of convergence to equilibrium, and central limit theorem in terms of the tail of the return time function.
Journal ArticleDOI
Almost Sure Invariance Principle for Nonuniformly Hyperbolic Systems
Ian Melbourne,Matthew Nicol +1 more
TL;DR: In this paper, the authors prove an almost sure invariance principle for general classes of nonuniformly expanding and non-uneiformly hyperbolic dynamical systems, and apply it to planar periodic Lorentz flows with finite horizon.
Journal ArticleDOI
Subexponential decay of correlations
TL;DR: In this article, a method for proving subexponential lower bounds for correlations functions was proposed, and applied to study the decay of correlations for maps with countable Markov partitions.
Journal ArticleDOI
Statistics of Return Times:¶A General Framework and New Applications
TL;DR: In this article, the authors provided general estimates for the errors between the distribution of the first, and more generally, the K − th return time (suitably rescaled) and the Poisson law for measurable dynamical systems.
Journal ArticleDOI
Large deviations for nonuniformly hyperbolic systems
Ian Melbourne,Matthew Nicol +1 more
TL;DR: In this paper, large deviation estimates for a large class of nonuniformly hyperbolic systems with summable decay of correlations were obtained, namely those modelled by Young towers.
References
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Journal ArticleDOI
Intermittent transition to turbulence in dissipative dynamical systems
Yves Pomeau,Paul Manneville +1 more
TL;DR: In this article, simple dissipative dynamical systems exhibiting a transition from a stable periodic behavior to a chaotic one were studied, where the inverse coherence time grows continuously from zero to zero due to the random occurrence of widely separated bursts in the time record.
Journal ArticleDOI
Statistical properties of dynamical systems with some hyperbolicity
TL;DR: In this article, the ergodic theory of attractors and conservative dynamical systems with hyperbolic properties on large parts (though not necessarily all) of their phase spaces is discussed.
Journal ArticleDOI
Recurrence times and rates of mixing
TL;DR: In this paper, the authors considered the setting of a map making "nice" return to a reference set, and defined criteria for the existence of equilibria, speed of convergence to equilibrium, and central limit theorem in terms of the tail of the return time function.
Journal ArticleDOI
On decay of correlations in Anosov flows
TL;DR: In this paper, the authors combine geometric considerations of Chernov with the thermodynamic formalism approach to construct an isomorphism between the diffeomorphism and a subshift of finite type and then prove that all such subshifts are exponentially mixing.
Journal ArticleDOI
Decay of correlations
TL;DR: In this article, Boyland, Boyland et al. presented a paper dedicated to Micheline Ishay, who would like to thank P. Collet and M. Wojtkowski for introducing me to the world of cones.
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Intermittent transition to turbulence in dissipative dynamical systems
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