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| PHYS0231-2 | An Approcah to Chaotic Phenomena
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| Duration : | 20h Th, 10h Pr |
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| Credits/ECTS : |
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| Holder(s) : | Pierre Dauby |
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| Language : | Langue française |
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| Course contents : | 1. Introduction and general considerations : Historical aspects. Dynamical systems. Stability of solutions. Structural stability. Local and global bifurcations. Definition of chaos. Predictibility and determinism. Universality of the transitions towards chaos. Examples of chaotic phenemena.
2. Tools to analyse chaos : Sensitive dependence on initial conditions. Strange attractors and fractal dimensions. Lyapounov exponents. Poincaré sections. Experimental reconstruction of attractors.
3. Routes towards chaos in dissipative systems : a. Period doublings. b. Quasi-periodicity (Landau and Ruelle-Takens theories, Circle maps, Frequecy-locking). c. Intermittency. d. Global bifurcations. e. Experiments.
4. Chaos in conservative systems.
5. Application : computer exercice. |
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| Organization : | The first part of the course (20 h) consists in the presentation of the theoretical material. The second part (10 h) consists in a homework (numerical analysis of a dynamical system). The timetable of the lectures is determined according to the students attending the course. |
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| Written notes : | Copies of transparencies. |
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| Assessment : | Oral exam on the theoretical material and short discussion on the homework. |
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| Contacts : | Pierre C. DAUBY, Chargé de cours
Institut de Physique (local 2/57), Bât. B5a, Allée du 6 août 17, B-4000 Liège 1
Tel. : 04/366.23.57 - Fax : 04/366.23.55 - Email : PC.Dauby@ulg.ac.be
www : http://www.ulg.ac.be/thermoir/Phenomenes_Chaotiques.htm |
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