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.
ASJC Scopus subject areas
- Applied Mathematics