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Differentiation of SRB States
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TLDR
In this paper, the Onsager reciprocity relations and the fluctuation-dissipation formula of nonequilibrium statistical mechanics have been studied in hyperbolic manifold diffeomorphisms.Abstract:
:Let f be a diffeomorphism of a manifold M, and ρf a (generalized) SRB state for f. If supp ρf is a hyperbolic compact set we show that the map is differentiable in a suitable functional setup, and we compute the derivative. When supp ρf is an attractor, the derivative is given by
where X is the vector field . This formula can be extended to time dependent situations and also, at least formally, to nonuniformly hyperbolic situations.
The above results will find their use in the study of the Onsager reciprocity relations and the fluctuation-dissipation formula of nonequilibrium statistical mechanics.read more
Citations
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References
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Ergodic theory of chaos and strange attractors
Jean-Pierre Eckmann,David Ruelle +1 more
TL;DR: A review of the main mathematical ideas and their concrete implementation in analyzing experiments can be found in this paper, where the main subjects are the theory of dimensions (number of excited degrees of freedom), entropy (production of information), and characteristic exponents (describing sensitivity to initial conditions).
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TL;DR: A survey article on the area of global analysis defined by differentiable dynamical systems or equivalently the action (differentiable) of a Lie group G on a manifold M is presented in this paper.
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Equilibrium states and the ergodic theory of Anosov diffeomorphisms
TL;DR: Gibbs Measures and Gibbs measures have been used in this article to define Axiom a Diffeomorphisms for general Thermodynamic Formalism and Ergodic Theory of Axiom-a-Diffeomorphism.
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Global Stability of Dynamical Systems
TL;DR: In this article, the authors present a Potpourri of stability results for Hyperbolic Sets and Markov Partitions for stable manifolds, as well as a list of notations.
Book ChapterDOI
The Ergodic Theory of Axiom A Flows.
Rufus Bowen,David Ruelle +1 more
TL;DR: In this article, the Whitney sum of three (Tf t )-invariant continuous subbundles of a Riemann manifold is used to define hyperbolic tangent bundles.