Dynamical quantities and their numerical analysis by saddle periodic orbits

We study estimators for dynamical quantities such as the topological entropy and the topological pressure which are based on numerical computations on periodic orbits. For the particular case of the Hénon family for some parameter ranges we find a reasonable convergence of the entropy, the pressure, and Birkhoff averages of test functions. However, pointing out possible pitfalls of such an analysis, we show that the evaluation by means of saddle orbits alone can be misleading if, for example, chaotic saddles and attractors coexist.