Non-linear dynamics and temporal chaos - Département de Physique de l'Ecole Normale supérieure

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Non-linear dynamics and temporal chaos

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November 14 - 18, 2022 :
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Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

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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

Enseignant : Laurette TUCKERMAN
Chargé de TD :
Physique de la matière condensée : Option
Physique macroscopique et complexité (ex physique des liquides : Option
Physique quantique : Option
Physique théorique : Option
ECTS : 3
Langue d’enseignement : Anglais
Site web : http://www.pmmh.espci.fr/ laurette/explanatory.html

Description

Bifurcation theory Pitchfork, saddle-node, transcritical and Hopf bifurcations
Jordan blocks and transient growth, global bifurcations

Thermal convection and the Lorenz model
Boussinesq approximation, linear stability analysis, Lorenz model

Symmetry
Reflection : symmetries of vector fields. Rotation : circle pitchfork and drift pitchfork
Groups : Zn and Dn, SO(2) and O(2). Equivariance and invariance, isotropy lattice
Standing and traveling waves in thermosolutal convection

Mappings and period-doubling
From continuous flows to discrete maps : Poincaré sections
Logistic mapping, Feigenbaum-Coullet-Tresser period-doubling cascade
Periodic windows : Sharkovskii’s Theorem
Floquet theory and fluid dynamics : Faraday instability, cylinder wake, convection

Quasiperiodicity and intermittency
Tori, circle maps, frequency locking, Arnold tongues, winding number, golden mean
Intermittency, Lyapunov exponents, Ruelle-Takens route to chaos

Stripes, Patterns and Instabilities Swift-Hohenberg equation.
Rolls, squares and hexagons.
Eckhaus and zig-zag instabilities

Fronts and reaction-diffusion systems
Turing patterns, excitable media, Lyapunov functionals, spatial analysis

Hamiltonian systems
Integrable systems : pendulum, twist maps, action-angle variables
Non-integrable perturbations : Poincaré-Birkhoff and KAM Theorems
Applications : three-body problem, billiards, blinking vortex

Nonlinear tourism
ODEs : Rossler system, van der Pol and Duffing oscillators
Maps : sine circle and Hénon map
Excitable media : FitzHugh-Nagumo, Barkley, Brusselator and Gray-Scott models
PDEs : Kuramoto-Sivashinsky, Swift-Hohenberg, Ginzburg-Landau equations

Quick links

Next student seminar :
Access to the program

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