Nonlinear Dynamics at the Free University Berlin

Summer 2008

BMS-Course Dynamical Systems III

Prof. Dr. Bernold Fiedler

Recitation session: Dr. Stefan Liebscher


Schedule, Summer 2008

Lecture:
Tuesday, 10.15-14.00, Seminar room 140, Arnimallee 7
Recitation session:
Monday, 12.15-14.00, Seminar room 140, Arnimallee 7

Topics

The course combines current concepts from Dynamical Systems and (mostly parabolic) Partial Differential Equations. Selection of Topics:

  1. Analytic Semigroups (survey)
  2. Invariant Manifolds
  3. Bifurcations
  4. Inertial Manifolds
  5. Global Attractors
  6. Spatio-Temporal Patterns

Web pages of parts I & II.

References

  • J. Hale: Functional differential equations, Applied Mathematical Sciences. Vol. 3, Springer, 1971
  • D. Henry: Geometric Theory of Semilinear Parabolic Equations, Springer, LNM 840, 1981
  • G. Sell, Y. You: Dynamics of evolutionary equations, Applied Mathematical Sciences 143, Springer, 2002
  • R. Temam: Infinite-Dimensional Systems in Mechanics and Physics, Springer, 1998.
  • M.I. Vishik: Asymptotic behaviour of solutions of evolutionary equations, Cambridge University Press, 1992
  • B. Fiedler, A. Scheel: Dynamics of Reaction-Diffusion Patterns. In: Trends in Nonlinear Analysis, Festschrift dedicated to Willi Jäger for his 60th birthday, M. Kirkilionis, R. Rannacher, F. Tomi (eds.), Springer, 2003, 23-152.
Script (corrections) on subharmonic bifurcation

Homework assignments, Summer 2008

  1. Abgabe: 25. April 2008 (PDF)
  2. Abgabe: 02. Mai 2008 (PDF)
  3. Abgabe: 08. Mai 2008 (PDF)
  4. Abgabe: 22. Mai 2008 (PDF)
  5. Abgabe: 29. Mai 2008 (PDF)
  6. Abgabe: 05. Juni 2008 (PDF)
  7. Abgabe: 12. Juni 2008 (PDF)
  8. Abgabe: 19. Juni 2008 (PDF)
  9. Abgabe: 26. Juni 2008 (PDF)
  10. Abgabe: 03. Juli 2008 (PDF)
  11. Abgabe: 10. Juli 2008 (PDF)

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