Nonlinear physics

Theoretical nonlinear physics I: Dynamical systems

Winter semester 2017/2018

Lecture with tutorials

Course number in the course overview: 110301 (lecture), 110302 (tutorials)

  • Lecturers, organization, dates & exams

    Lecturer

    Prof. Dr. U. Thiele

    ITP, Wilhelm-Klemm-Straße 9, 48149 Münster, room 315
    Tel.: +49 251 83-34939, email: u.thiele(at)uni-muenster.de

    Dates & Locations

    Lecture Tue., 14:15–15:45 KP/TP 304
    Start: Tue., 10.10.2017
    Tutorials Wed., 08:15–09:45 (every second week) KP/TP 303
    Beginn: by arrangement
  • Contents & literature

    Contents of the lecture

    This is part I of Theoretical Nonlinear Physics, whose focus are the dynamical systems, i. e., mathematically finite-dimensional systems with purely temporal dynamics. In the following summer semester, part II will follow with a focus on pattern formation in spatially extended systems, i. e. we consider mathematically infinite-dimensional systems with space–time dynamics.

    The individual chapters of part I are:

    • Introduction
    • Experiments and models
    • Dynamical systems – distinctions and concepts
    • The logistic map
    • Flows – linear stability analysis
    • Flows – bifurcations and weakly nonlinear analysis
    • Deterministic chaos – properties and emergence

    Literature

    Dynamical systems

    • Argyris, J., Faust, G., Haase, M., and Friedrich, R. (2015). An Exploration of Dynamical Systems and Chaos: Completely Revised and Enlarged Second Edition, Springer Berlin Heidelberg.
    • Iooss, G. & Joseph, D. (2012). Elementary Stability and Bifurcation Theory, Springer.
    • Murray, J. D. (1993). Mathematical Biology, Springer Verlag, Berlin.
    • Ott, E. (2002). Chaos in Dynamical Systems, Cambridge University Press.
    • Strogatz, S. H. (1994). Nonlinear Dynamics and Chaos, Addison-Wesley.

    Nonlinear systems – general

    • Ebeling, W. and Feistel, R. (2011). Physik der Selbstorganisation und Evolution. Wiley-VCH Verlag, Weinheim.
    • Nicolis, G. (1999). Introduction to nonlinear science. Cambridge University Press.
    • Nicolis, G. and Prigogine, I. (1977). Self-Organization in Nonequilibrium Systems: From Dissipative Structures to Order through Fluctuations. John Wiley & Sons.
    • Pismen, L. (2006). Patterns and Interfaces in Dissipative Dynamics (Springer Series in Synergetics). Springer.
    • Scott, A. (2006). Encyclopedia of Nonlinear Science. Taylor & Francis.

    more literature in the lecture

  • Lecture material

    Materials for the lecture will be provided in the Learnweb

  • Tutorials

    Coordination: Walter Tewes

  • Problem sheets

    Exercise sheets will be provided in the Learnweb