Application of hyperbolic dynamics to physics: Some problems and conjectures

DOI10.1090/S0273-0979-04-01023-7zbMath1102.37051WikidataQ122999484 ScholiaQ122999484MaRDI QIDQ4813563

David Pierre Ruelle

Publication date: 13 August 2004

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

long-time behaviordependence on parametersanalytic continuationSRB measuresmooth dynamical systems

Mathematics Subject Classification ID

Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Classical dynamic and nonequilibrium statistical mechanics (general) (82C05)

Related Items (12)

Linear response function for coupled hyperbolic attractors ⋮ Response theory for equilibrium and non-equilibrium statistical mechanics: Causality and generalized Kramers-Kronig relations ⋮ On the susceptibility function of piecewise expanding interval maps ⋮ Whitney-Hölder continuity of the SRB measure for transversal families of smooth unimodal maps ⋮ Natural boundary for the susceptibility function of generic piecewise expanding unimodal maps ⋮ Hilbert spaces of martingales supporting certain substitution-dynamical systems ⋮ Alternative proofs of linear response for piecewise expanding unimodal maps ⋮ Structure and \(f\)-dependence of the a.c.i.m. for a unimodal map \(f\) of Misiurewicz type ⋮ Mathematical foundation of nonequilibrium fluctuation-dissipation theorems for inhomogeneous diffusion processes with unbounded coefficients ⋮ Analyticity of the SRB measure for holomorphic families of quadratic-like Collet-Eckmann maps ⋮ Analytical techniques for linear response formula of equilibrium states ⋮ Differentiating the absolutely continuous invariant measure of an interval map \(f\) with respect to \(f\)

Cites Work

• The dynamics of the Hénon map
• Differentiation of SRB states
• On differentiability of SRB states for partially hyperbolic systems
• Strange attractors in higher dimensions
• Strange attractors with one direction of instability
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