ESAM 421-3 |

Spring 2001 |

Prof. H. Riecke |

Outline |

- Hamiltonian dynamics
- Hamilton's principle
- Hamiltonian formulation
- General properties of Hamiltonian dynamics

- Transformation theory
- Canonical transformations
- Hamilton-Jacobi equation. Action-angle variables
- Integrable systems: tori
- Symmetries and conserved quantities

- Maps I
- Perturbation theory
- Regular perturbation theory for ODE
- Canonical perturbation theory: N = 1
- Canonical perturbation theory: N > 1

- KAM-theorem
- Example of a superconvergent perturbation theory
- How irrational is an irrational number

- Maps II
- Twist maps
- Poincaré-Birkhoff fixed-point theorem
- The fate of heteroclinic orbits

- Kneading of dough as chaotic system
- Reviewing sketch of thermodynamics
- Statistical ensembles
- Microcanonical ensemble
- Canonical ensemble
- Phase transitions
- Magnetism and Ising model
- Ising model in d = 1
- Mean-field theory

Recommended books:

M. Tabor, *Chaos and Integrability in Nonlinear Dynamics*

I. Percival and D. Richards, *Introduction to Dynamics*

J.B. Marion, *Classical Dynamics of Particles and Systems*

H. Goldstein, *Classical Mechanics*

A.J. Lichtenberg and M.A. Lieberman, *Regular and Stochastic Motion*

J. Guckenheimer and P. Holmes, *Nonlinear Oscillations, Dynamical Systems,
and Bifurcations of Vector Fields*

These books will be on reserve.

There will be homework assignments which will be graded. There will be no midterm or final.

Office Hours:

M 3:30-4, 5-5:30

We 3:30-5:30

in M458

e-mail: h-riecke@northwestern.edu

Homework assignments:

HW 1 HW 2 HW 3 HW 4

Some remarks on HW 4.

File translated from T

On 26 Mar 2001, 09:21.