Transition maps at non-resonant hyperbolic singularities are o-minimal... complete and o-minimal expansion of the field of realnumbers such that, for any planar analytic vector field X and any isolated,non-resonant hyperbolic singularity p of X, a transition map for X at p isdefinable in this structure....
Smoothness of transition maps in singular perturbation problems with one fast variable AbstractThis paper deals with the smoothness of the transition map between two sections transverse to the fast flow of a singularly perturbed vector field (one fast, multiple slow directions)....
Transition map and shadowing lemma for normally hyperbolic invariant manifolds...whose stable andunstable manifolds intersect transversally, we consider several tools andtechniques to detect trajectories with prescribed itineraries: the scatteringmap, the transition map, the method of correctly aligned windows, and theshadowing lemma....
Transition map and shadowing lemma for normally hyperbolic invariant manifolds... For a given a normally hyperbolic invariant manifold, whose stable and unstable manifolds intersect transversally, we consider several tools and techniques to detect orbits with prescribed trajectories: the scattering map, the transition map, the method of correctly aligned windows, and the shadowing lemma....
