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LES: Surfaces of section and the Henon trick

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25 april 2017 17:00
NB 5114.0004


Surfaces of section are frequently used in studies of $n$-dimensional continuous dynamical systems with $n\geq3$. The dynamics of the system an be understood via a Poincare return map that defines a discrete dynamical system of dimension $n-1$ on the surface. We will have a look at a couple examples of $3$-dimensional systems and the challenges one faces when defining return maps. In chaotic systems we will then appreciate the simplicity and power of the so-called Henon trick published in M. Henon's 1982 paper. At the end of the talk you'll be able to understand and enjoy a couple nice pictures that would not have been possible without the use of the Henon trick.

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