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Title: The center-focus and ciclicity problems: an implementation of the Lyapunov method and the interpolation technique
Author: Sánchez Sánchez, Iván
Director: Rodríguez Velázquez, Juan Alberto
Tutor: Villadelprat Yagüe, Jordi
Torregrosa Arús, Joan
Others: Universitat Oberta de Catalunya
Keywords: polynomial differential equations
center characterization
Lyapunov quantities
Issue Date: Sep-2017
Publisher: Universitat Oberta de Catalunya
Abstract: The 16th Hilbert problem aims to determine the maximum number of isolated periodic solutions which a system of polynomial differential equations in the plane has. A first approach to this are the center-focus and ciclicity problems, which consist in identifying whether the origin of a system is a center or a focus and determining the maximum number of limit cycles, respectively. Here, we aim to study these problems for polynomial differential equations and this means to analyze the stability in a neighbourhood of a monodromic non-degenerate point. An essential mathematical object to deal with these issues are the Lyapunov quantities, which determine whether the origin is a center or a focus and its stability.
Language: English
Appears in Collections:Bachelor thesis, research projects, etc.

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