Dynamical systems and chaos - Département de Physique de l'Ecole Normale supérieure

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Dynamical systems and chaos

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Lectures: Stephan Fauve
Exercises: Baptiste Coquinot
ECTS credits: 3
Language of instruction : English
Key words: Dynamical systems, instabilities, fluctuations, stochastic processes
Exam: written

Description

These lectures concern deterministic dynamical systems, i.e. systems governed by coupled differential equations. Most dynamical problems in physics and elsewhere can be modeled that way. Interesting dynamics occur when the governing equations are nonlinear which is the usual case. In contrast to linear systems, nonlinear ones generally have multiple solutions of different qualitative nature, for instance different symmetries. The stability of these solutions is modified at bifurcation points when a control parameter of the system is changed. We will show that universal behaviors are observed in the vicinity of these bifurcations mostly dependent on symmetries. We will then show how a sequence of successive bifurcations can lead to chaos, i.e. a random dynamical behavior although the system is governed by deterministic rules. We will finally present some methods to analyze chaotic regimes.

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Next student seminar :
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Here you can find information about your internships:
Experimental Internship - Undergraduate program
Master ICFP first year Internship

News : ICFP Research seminars
November 14 - 18, 2022 :
All information about the program

Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr