  We construct countable Markov partitions for non-uniformly hyperbolic
diffeomorphisms on compact manifolds of any dimension, extending earlier work
of O. Sarig for surfaces. These partitions allow us to obtain symbolic coding
on invariant sets of full measure for all hyperbolic measures whose Lyapunov
exponents are bounded away from zero by a constant. Applications include
counting results for hyperbolic periodic orbits, and structure of hyperbolic
measures of maximal entropy.
