Compact locally maximal hyperbolic sets are studied via geometrically defined functional spaces that take advantage of the smoothness of the map in a neighborhood of the hyperbolic set. This provides a self-contained theory that not only reproduces all the known classical results, but also gives new insights on the statistical properties of these systems.
"Compact locally maximal hyperbolic sets for smooth maps: fine statistical properties." J. Differential Geom. 79 (3) 433 - 477, July 2008. https://doi.org/10.4310/jdg/1213798184