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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/24935

Title: Semi-local normal forms of saddle connections and a study of non-elementary singularities
Authors: Wynen, Jeroen
Advisors: De Maesschalck, Peter
Bonckaert, Patrick
Naudot, Vincent
Issue Date: 2017
Abstract: We develop tools to study the transition in planar vector fields near non-elementary singularities. In particular we focus on symmetric connections which appear naturally in blow-up phase portraits and the circle at infinity. First we develop a semi-local normal form which is applicable near the connection. Then we add some non-smooth variables such that we can normally linearize the system. This allows us to express the transition map near the connection in terms of a finite amount of variables and we provide an asymptotic expansion of the transition map. Finally, we apply the results to homoclinic connections containing a non-elementary singularity, in this case a cusp or a fake saddle.
URI: http://hdl.handle.net/1942/24935
Category: T1
Type: Theses and Dissertations
Appears in Collections: PhD theses
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