AM 0219: Nonlinear Dynamical Systems

Fall 2004, Brown University, Division of Applied Mathematics

AM 0219: Nonlinear Dynamical Systems - Theory and Applications

Prof. Dr. Bernold Fiedler, Dr. Stefan Liebscher

Classes

180 George Street, Room 106
Mon, 3:00 pm - 4:30 pm
Wed, 11:15 am - 12:30 pm

Recitation

180 George Street, Room 106
Wed, 10:15 am - 11:05 am

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

  • K.T. Alligood, T.D. Sauer, and J.A. Yorke: Chaos, Springer, 1997.
  • H. Amann: Ordinary Differential Equations, de Gruyter 1990.
  • V.I. Arnold: Ordinary Differential Equations, Springer.
  • W.E. Boyce and R.C. DiPrima: Elementary Differential Equations and Boundary Value Problems, Wiley, 5th edition, 1992.
  • E.A. Coddington and N. Levinson: Theory of Ordinary Differential Equations, McGill-Hill, 1955.
  • Dynamical Systems I, ed.: D.K. Anosov and V.I. Arnold, Encyclopaedia of Mathematical Sciences Vol 1, Springer, 1988.
  • J. Hale: Ordinary Differential Equations, Wiley, 1969.
  • P. Hartmann: Ordinary Differential Equations, Wiley, 1964.
  • M.W. Hirsch and S. Smale: Differential equations, dynamical systems, and linear algebra, Academic Press, 1974.
  • F. Verhulst: Nonlinear Differential Equations and Dynamical Systems, Springer, 2nd edition, 1996.

Exercises

Notes

Links