AG Linz: Strukturbildung & Nichtlineare Dynamik

THEORETICAL NONLINEAR PHYSICS 1 (TNLP1), Fall/Winter 2020/21 (Prof. S.J. Linz)

last update (Oct 26, 2020)
Due to the rising number of corona infections in MS (today's 7 day incidence
is above 62), the class and the tutorials will be taught online via ZOOM.
Our central base is the Learnweb page TNLP 1.
Students who like to attend the class should contact me by email (slinz@wwu.de)
to obtain the password.

lectures: Tuesdays 14-16

ZOOM meetings, details and access can be found on the Learnweb page
start on Nov. 3, 2020

The first part (TNLP I) deals primarily with nonlinear dynamical systems, i.e. systems
of ODEs and maps with purely temporal dynamics and their application in science,
whereas the second part (TNLP II) taught in the Spring/Summer semester focusses
on pattern forming systems (PDE with generally spatio-temporal dynamics)

The class and the tutorials will be taught in English, unless all students agree
that they should be taught in German.

There will be a Learnweb page for the class with extra material

planned topics

- Intro: nonlinear behavior in science and technology
- dynamical systems, orbits, state space, flow, attractors
- essential theorems for dynamical systems
- organisation of the flow in state space
- stability analysis
- elementary bifurcation theory
- center manifold and normal form theory
- asymptotic methods for the calculation of orbits
- Lyapunov spectrum and chaotic behavior
- reduction methods: Poincare maps
- basic properties of iterated maps, routes to chaos

literature (the classics):
- E.A. Jackson, Perspectives of Nonlinear Dynamics I+II, Cambridge Univ. Press 1992
- V. I. Arnol'd, Ordinary Differential Equations, MIT Press 1998
- E. Ott, Chaos in Dynamical Systems, Cambridge Univ. Press 1993
- S.H. Strogatz, Nonlinear Dynamics And Chaos, Westview Press 1994