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Noncommutative algebras for hyperbolic diffeomorphisms

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Summary

The Gibbs states of classical equilibrium statistical mechanics can be extended to states on non commutative algebras, satisfying the Kubo-Martin-Schwinger boundary condition. This way of looking at Gibbs states is applied here to the study of differentiable dynamical systems when some (strong or weak) hyperbolicity conditions are satisfied.

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  1. David Ruelle

    Present address: Institut des Hautes Etudes Scientifiques, 35, route de Chartres, F-91440, Bures-sur-Yvette, France

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    1. David Ruelle
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    This manuscript was completed while the author was visiting the California Institute of Technology as a Fairchild Scholar.

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    Ruelle, D. Noncommutative algebras for hyperbolic diffeomorphisms. Invent Math 93, 1–13 (1988). https://doi.org/10.1007/BF01393685

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