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Publications Influence

A new test for chaos in deterministic systems

- G. Gottwald, I. Melbourne
- Mathematics, Physics
- Proceedings of the Royal Society of London…
- 26 August 2002

We describe a new test for determining whether a given deterministic dynamical system is chaotic or non–chaotic. In contrast to the usual method of computing the maximal Lyapunov exponent, our method… Expand

351 24- PDF

On the Implementation of the 0-1 Test for Chaos

- G. Gottwald, I. Melbourne
- Computer Science, Mathematics
- SIAM J. Appl. Dyn. Syst.
- 9 January 2009

TLDR

228 20- PDF

Asymptotic stability of heteroclinic cycles in systems with symmetry. II

- M. Krupa, I. Melbourne
- Mathematics
- 1 December 2004

Systems possessing symmetries often admit robust heteroclinic cycles that persist under perturbations that respect the symmetry. In previous work, we began a systematic investigation into the… Expand

84 19

An example of a non-asymptotically stable attractor

- I. Melbourne
- Mathematics
- 1991

56 12

Testing for Chaos in Deterministic Systems with Noise

- G. Gottwald, I. Melbourne
- Mathematics, Physics
- 15 October 2004

Abstract Recently, we introduced a new test for distinguishing regular from chaotic dynamics in deterministic dynamical systems and argued that the test had certain advantages over the traditional… Expand

191 11- PDF

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

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

The Lorenz Attractor is Mixing

- S. Luzzatto, I. Melbourne, F. Paccaut
- Mathematics, Physics
- 8 October 2004

We study a class of geometric Lorenz flows, introduced independently by Afraimovič, Bykov & Sil′nikov and by Guckenheimer & Williams, and give a verifiable condition for such flows to be mixing. As a… Expand

91 7- PDF

Large and moderate deviations for slowly mixing dynamical systems

- I. Melbourne
- Mathematics
- 26 November 2008

We obtain results on large deviations for a large class of nonuniformly hyperbolic dynamical systems with polynomial decay of correlations , . This includes systems modelled by Young towers with… Expand

68 7- PDF

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