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Publications Influence

Almost Sure Invariance Principle for Nonuniformly Hyperbolic Systems

- I. Melbourne, M. Nicol
- Mathematics
- 29 March 2005

We prove an almost sure invariance principle that is valid for general classes of nonuniformly expanding and nonuniformly hyperbolic dynamical systems. Discrete time systems and flows are covered by… Expand

154 11- PDF

A vector-valued almost sure invariance principle for hyperbolic dynamical systems

- I. Melbourne, M. Nicol
- Mathematics
- 21 June 2006

We prove an almost sure invariance principle (approximation by d-dimensional Brownian motion) for vector-valued Holder observables of large classes of nonuniformly hyperbolic dynamical systems. These… Expand

92 9- PDF

Extremes and Recurrence in Dynamical Systems

- V. Lucarini, D. Faranda, +6 authors S. Vaienti
- Mathematics, Physics
- 25 April 2016

This book provides a comprehensive introduction for the study of extreme events in the context of dynamical systems. The introduction provides a broad overview of the interdisciplinary research area… Expand

99 8- PDF

Large deviations for nonuniformly hyperbolic systems

- I. Melbourne, M. Nicol
- Mathematics
- 2008

We obtain large deviation estimates for a large class of nonuniformly hyperbolic systems: namely those modelled by Young towers with summable decay of correlations. In the case of exponential decay… Expand

136 7- PDF

Acceleration of one-dimensional mixing by discontinuous mappings

The paper considers a simple class of models for mixing of a passive tracer into a bulk material that is essentially one dimensional. We examine the relative rates of mixing due to diffusion, stretch… Expand

32 6

Polynomial loss of memory for maps of the interval with a neutral fixed point

- R. Aimino, H. Hu, M. Nicol, A. Torok, S. Vaienti
- Mathematics
- 18 February 2014

We give an example of a sequential dynamical system consisting of intermittent-type maps which exhibits loss of memory with a polynomial rate of decay. A uniform bound holds for the upper rate of… Expand

32 6- PDF

Annealed and quenched limit theorems for random expanding dynamical systems

- R. Aimino, M. Nicol, S. Vaienti
- Mathematics
- 16 October 2013

In this paper, we investigate annealed and quenched limit theorems for random expanding dynamical systems. Making use of functional analytic techniques and more probabilistic arguments with… Expand

37 4- PDF

Symmetry of attractors and the Karhunen-Loegve decomposition

- M. Dellnitz, M. Golubitsky, M. Nicol
- Physics
- 16 May 1994

Recent fluid dynamics experiments [13, 10, 4] have shown that the symmetry of attractors can manifest itself through the existence of spatially regular patterns in the time average of an appropriate… Expand

47 3

A Borel-Cantelli lemma for nonuniformly expanding dynamical systems

- Chinmaya Gupta, M. Nicol, W. Ott
- Mathematics
- 12 July 2010

Let be a sequence of sets in a probability space such that . The classical Borel–Cantelli (BC) lemma states that if the sets An are independent, then μ({x X : x An for infinitely many values of n}) =… Expand

19 3- PDF

Almost sure invariance principle for sequential and non-stationary dynamical systems

- N. Haydn, M. Nicol, A. Torok, S. Vaienti
- Mathematics
- 17 June 2014

We establish almost sure invariance principles, a strong form of approximation
by Brownian motion, for non-stationary time-series arising as observations
on dynamical systems. Our examples include… Expand

44 3- PDF

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