Fontich, E.; Simó, C. Invariant manifolds for near identity differentiable maps and splitting of separatrices. (English) Zbl 0706.58060 Ergodic Theory Dyn. Syst. 10, No. 2, 319-346 (1990). The aim of this paper is the study of the asymptotic behaviour of invariant manifolds, for families of differentiable diffeomorphisms with hyperbolic points, close to the identity, which tend to it when the parameter goes to zero. So, the authors prove that the invariant manifolds tend, in a certain sense, when the diffeomorphisms tend to the identity, to the invariant manifolds of a critical point of a vector field which is constructed in association with the family. As a consequence of these results, the families of near identity two- dimensional diffeomorphisms with a hyperbolic point and homoclinic points associated with it are considered and the maximum separation between the invariant manifolds is found. It is of the order of some power of the parameter which is related to the degrees of differentiability. Reviewer: L.Maxim-Răileanu Cited in 2 ReviewsCited in 15 Documents MSC: 37C80 Symmetries, equivariant dynamical systems (MSC2010) 37C10 Dynamics induced by flows and semiflows Keywords:invariant manifolds; hyperbolic point; homoclinic points × Cite Format Result Cite Review PDF