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

Why choose this program? Program, courses and calendar Master ICFP 1st year (2023-2024) 2023-2024 Calendar and timetable Courses Internships Program, courses and calendar Master ICFP 1st year (2022-2023) 2022-2023 Calendar and timetable Courses Internships Program, courses and calendar Master ICFP 2nd year 2023-2024 First Semester Second Semester "Physics Now" Seminars 2019/2020 "Physics Now" Seminars 2020/2021 "Physics Now" Seminars 2021/2022 "Physics Now" Seminars 2023/2024 "Physics Now" Seminars 2022/2023 Internships 2023 2024 calendar Program, courses and calendar Master ICFP 2nd year 2022-2023 First Semester Second Semester "Physics Now" Seminars 2019/2020 "Physics Now" Seminars 2020/2021 "Physics Now" Seminars 2021/2022 "Physics Now" Seminars 2022/2023 Internships 2022 2023 calendar Admission and Language Requirements How to apply Information for students Information for International Students Fees and Scholarships Careers Master Intranet Archives Erreur ( A supprimer) Program, courses and calendar Master ICFP 1st year (2021-2022) Program, courses and calendar Master ICFP 1st year (2021-2022) Program, courses and calendar Master ICFP 2nd year 2021-2022 Program, courses and calendar Master ICFP 2nd year 2020-2021 Program, courses and calendar Master ICFP 2nd year 2019-2020 Archives 2015-2016 Archives 2016-2017 Archives 2017-2018 Archives 2018-2019 Archives 2019-2020 Archives 2020-2021

Non-linear dynamics and temporal chaos

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

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

Faculty: Laurette TUCKERMAN
Tutor:
Condensed Matter Physics: Option
Macroscopic Physics and Complexity: Option
Quantum Physics: Option
Theoretical Physics: Option
ECTS credits: 3
Langue d’enseignement: English
Web site: 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