Counting orbits in conjugacy classes of the Henon Hamiltonian repeller

We present exact formulas solving the problem of partitioning the total number Mk of period-k orbits of the area-preserving Henon map into the number of orbits building its three possible conjugacy classes. The formulas are valid for any arbitrary period k. They are derived with combinatorial methods and constitute a nice application of the number-theoretic Mobius inversion formula to a key problem in physics and dynamical systems. A handy MAPLE implementation of the formulas is also provided