Abstract

Lyapunov exponents, entropy, and dimension play a major role in the ergodic theory of hyperbolic dynamics. Moreover, they are related in a very precise manner, giving rise to what I call dimension formulas. My aim is to discuss these relations, both for hyperbolic sets and hyperbolic measures, and to show that they can be obtained using tools from the foundations of hyperbolic dynamics and ergodic theory. I will also present a simple proof of a dimension formula for hyperbolic sets. The talk will be self-contained.