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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. | Keywords: | dynamical systems; normal forms; Hilbert 16th problem; saddle connections; transition maps | Document URI: | http://hdl.handle.net/1942/24935 | Category: | T1 | Type: | Theses and Dissertations |
Appears in Collections: | PhD theses Research publications |
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Thesismetvoorblad.pdf | 1.5 MB | Adobe PDF | View/Open |
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