The "0 to ∞-homoclinic bifurcation" of a class of discrete two-dimensional maps - Battelli, Flaviano; Lazzari, Claudio (Annales Mathematicae Silesianae, 1999)
Based on a previous theoretical result of the same authors the presen paper deals with discrete perturbed two-dimensional maps having a semi-hyperbolic fixed point. We give applicable sufficient conditions assuring a particular kind of bifurcation of homoclinic orbits when the perturbative parameter μ varies in a small neighborhood of zero: no homoclinic orbits when μ is on one side of zero, one homoclinic orbit when μ = 0, and infinite homoclinics when μ is on the other side of zero.