Statistical properties of piecewise smooth hyperbolic systems in high dimensions
This paper deals with smooth hyperbolic systems with singularities and their SRB measures. Note that SRB measures are the only physically observable invariant measures for smooth or piecewise smooth hyperbolic dynamical systems. The author assumes that the singularities are submanifolds and proves both the existence of ergodic SRB measures and its mixing and statistical properties. The main results of this paper, however, are statistical properties -- the exponential bound on correlations and the central limit theorem.
scientific article; zbMATH DE number 1492576