Random perturbations and statistical properties of Hénon-like maps
Let f be a smooth self-map of an m-dimensional (m ≥ 4) closed connected and simply-connected manifold such that the sequence of the Lefschetz numbers of its iterations is periodic. For a fixed natural r we wish to minimize, in the smooth homotopy class, the number of periodic points with periods less than or equal to r. The resulting number is given by a topological invariant J[f] which is defined in combinatorial terms and is constant for all sufficiently large r. We compute J[f] for self-maps...
We are interested in the optimality of monotonicity criteria for the period function of some planar Hamiltonian systems. This study is illustrated by examples.