Quadratic Area Preserving Maps in R². Lliçó inaugural del curs acadèmic 2013-2014. Facultat de Matemàtiques
Matèria: Matemàtiques
Format: 17 x 24
Pàgines: 44
Data d'edició: 2013
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Quadratic Area Preserving Maps in R². Lliçó inaugural del curs acadèmic 2013-2014. Facultat de Matemàtiques
Carles Simó
The author considers the description, explanation and prediction of the properties of the orbits of a given system as one of the main goals of Dynamical Systems. In this lecture he focuses on the quadratic Area Preserving Maps (APM) in R2. There are several reasons for this choice. It is a paradigmatic model. Many problems concerning: the existence of invariant curves diffeomorphic to a circle; the role of invariant manifolds of hyperbolic fixed or periodic points and how they lead to the existence of chaos; the geometrical mechanisms leading to the destruction of invariant curves; and quantitative measures of different properties for general APM, can all be understood thanks to our knowledge of the quadratic case. A review of these topics is presented in the lecture. Several open questions and extensions are shown at the end of this lecture.
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