Normal linearization and transition map near a saddle connection with symmetric resonances

We consider a heteroclinic connection in a planar system, between two symmetric hyperbolic saddles of which the eigenvalues are resonant. Starting with a C-infinity normal form, defined globally near the connection, we normally linearize the vector field by using finitely smooth tags of logarithmic form. We furthermore define an asymptotic entry-exit relation, and we discuss on two examples how to deal with counting limit cycles near a limit periodic set involving such a connection. (C) 2017 Elsevier Inc. All rights reserved.

Publication year:2018

Keywords:Planar vector fields, Saddle connection, Invariant, Linearization, Cyclicity, Poincaré map, Poincare map

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BOF-publication weight:6

CSS-citation score:1

Authors:International

Authors from:Higher Education

Accessibility:Open