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Spring 2005, Brown University, Division of Applied Mathematics
AM 0220: Nonlinear Dynamical Systems - Theory and Applications
Prof.
Dr. Bernold Fiedler,
Dr.
Stefan Liebscher
Classes
37 Manning Walk, Room 104
Mon, Wed 3:00 pm - 4:20 pm
Exception: Wed, Feb 09 in 182 George Street, Room 110
Recitation
180 George Street, Room 106
Wed, 1:00 pm - 1:50 pm
Overview
Basic theory of ordinary differential equations, flows, and maps.
Two-dimensional systems. Linear systems. Hamiltonian and integrable systems.
Lyapunov functions and stability.
Invariant manifolds, including stable, unstable, and center manifolds.
Bifurcation theory and normal forms.
Nonlinear oscillations and the method of averaging.
Chaotic motion, including horseshoe maps and the Melnikov method.
Applications in the physical and biological sciences.
References
- V. I. Arnold: Geometrical methods in the theory of ordinary
differential equations, Springer, 1983.
- C. Chicone: Ordinary differential equations with applications.
Springer.
- S. N. Chow and J.K.Hale: Methods of Bifurcation Theory,
Springer, 1982.
- W. de Melo and S. van Strien: One-dimensional dynamics,
Birkhäuser, 1993.
- R. L. Devaney: An introduction to chaotic dynamical systems,
Perseus Books, 1989.
- J. Guckenheimer and P.Holmes: Nonlinear Oscillations, dynamical
systems and bifurcations of vector fields, Springer, 1983.
- P. Hartmann: Ordinary Differential Equations,
Birkhäuser, 1982
- G. Iooss and M. Adelmeyer: Topics in bifurcation theory and
application, World Scientific, 1992.
- A. Katok, and B. Hasselblatt: Introduction to the Modern Theory
of Dynamical Systems, Cambridge University Press, 1995.
- Y. Kuznetsov: Elements of Applied Bifurcation Theory,
Springer, 1995.
- J. Moser: Stable and Random Motions in Dynamical Systems,
Princeton University Press, 1973.
- A. Vanderbauwhede: Centre Manifolds, Normal Forms, and Elementary
Bifurcations, in U. Kirchgraber and H. O. Walther, editors:
Dynamics Reported 2, Teubner & Wiley, 1989.
- Encyclopedia of Math. Sci., Dynamical Systems. Vol I-IX.
Springer.
Exercises
Notes
Links
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