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Application of hyperbolic dynamics to physics: Some problems and conjectures


Author: David Ruelle
Journal: Bull. Amer. Math. Soc. 41 (2004), 275-278
MSC (2000): Primary 37C40; Secondary 37D45
DOI: https://doi.org/10.1090/S0273-0979-04-01023-7
Published electronically: April 13, 2004
MathSciNet review: 2058287
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Abstract | References | Similar Articles | Additional Information

Abstract: The long time behavior of smooth dynamical systems is, in good cases, given by an SRB measure $\rho$. The measure $\rho$ is expected often to have very discontinuous dependence on parameters of the dynamical system. This is a very unsatisfactory situation for physical applications, where one would like to differentiate $\rho$ with respect to parameters. Here we propose a solution to this difficulty, based on analytic continuation in a frequency variable $\omega$.


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Additional Information

David Ruelle
Affiliation: Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019
Address at time of publication: IHES, 91440 Bures sur Yvette, France
Email: ruelle@ihes.fr

DOI: https://doi.org/10.1090/S0273-0979-04-01023-7
Keywords: Smooth dynamics, SRB states
Received by editor(s): October 1, 2003
Published electronically: April 13, 2004
Dedicated: René Thom in memoriam.
Article copyright: © Copyright 2004 American Mathematical Society

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