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The pressure and higher correlations for an Anosov diffeomorphism

Published online by Cambridge University Press:  04 June 2001

MOTOKO KOTANI  and
TOSHIKAZU SUNADA
MOTOKO KOTANI
Affiliation:
Mathematical Institute, Graduate School of Sciences, Tohoku University, Aoba, Sendai 980-77, Japan (e-mail: {kotani,sunada}@math.tohoku.ac.jp)
TOSHIKAZU SUNADA
Affiliation:
Mathematical Institute, Graduate School of Sciences, Tohoku University, Aoba, Sendai 980-77, Japan (e-mail: {kotani,sunada}@math.tohoku.ac.jp)
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Abstract

For a topologically mixing Anosov diffeomorphism on a compact manifold, the correlation function for two smooth functions is known to have exponential decay. As a generalization, higher correlation functions for several smooth functions are defined, and are shown to have exponential decay in the time variables. It is also proved that the higher derivatives of the pressure are equal to the summations of the higher correlations over the time variables.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 3 , June 2001 , pp. 807 - 821
Copyright
2001 Cambridge University Press

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