Characterization of unstable periodic orbits in chaotic attractors and repellers

A numerical technique for the characterization of the chaotic regime of dissipative maps through unstable periodic orbits is presented. It is shown that although the maps are dissipative their trajectories can be derived from a Hamiltonian, which allows us to calculate unstable periodic orbits of arbitrary length finding all points to any desired accuracy. Applying the method to the Hénon map we found that in a previously unexplored region of parameter space the topological entropy exhibits plateaus on which it is constant while the dynamics is characterized by a strange repeller.