Aplicacions quadràtiques que preserven l'àrea a R²

Authors

  • Carles Simó

Abstract

I consider 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 we focus 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 the lecture.

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Published

2014-09-10

How to Cite

Simó, C. (2014). Aplicacions quadràtiques que preserven l’àrea a R² . Butlletí De La Societat Catalana De Matemàtiques, 29(1), 77–108. Retrieved from https://revistes.iec.cat/index.php/BSCM/article/view/85830.001

Issue

Vol. 29 No. 1 (2014)

Section

Articles

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