Heteroclinic orbits, mobility parameters and stability for thin film type equations.
Heterodimensional cycles, partial hyperbolicity and limit dynamics
We study one-parameter families of diffeomorphisms unfolding heterodimensional cycles (i.e. cycles containing periodic points of different indices). We construct an open set of such arcs such that, for a subset of the parameter space with positive relative density at the bifurcation value, the resulting nonwandering set is the disjoint union of two hyperbolic basic sets of different indices and a strong partially hyperbolic set which is robustly transitive. The dynamics of the diffeomorphisms we...
Higher dimensional Melnikov mappings
Higher order branching of periodic orbits from polynomial isochrones.
Higher-order Melnikov functions for single-DOF mechanical oscillators: theoretical treatment and applications.
Homoclinic orbit solutions of a one dimensional Wilson-Cowan type model.
Homoclinic tangencies and hyperbolicity for surface diffeomorphisms.
Homoclinics : Poincaré-Melnikov type results via a variational approach