Chaos and Its Applications
615.765

Course Description
This course provides a topical introduction to the basic concepts and active areas of modern nonlinear dynamics, including sensitive dependence on initial conditions, fractals, routes to chaos, experimental techniques, symbolic dynamics, and control of chaos in real systems. The course emphasizes applications to and examples from physics and engineering, including geophysical systems, electronic oscillators, mechanical engineering, and information science. Although some mathematical theory is necessary to develop the material, extensive use of concrete examples helps to enhance necessary intuition. Students conduct numerical experiments using provided software, which allows for interactive learning. Access to Whiting School computers is provided for those without appropriate personal computers.

Syllabus

1. Introduction and motivational examples
2. Stability of dynamical systems
3. One-dimensional maps and periodic orbits
4. Strange sets / fractal dimensions
5. Connections between dimensions and dynamics
6. Applications: celestial mechanics, cardiology, communications, lasers
7. Routes to chaos I: period doubling; intermittency; crises and the sinking of Harald of Free Enterprize
8. Routes to chaos II: quasiperiodicity and turbulence (Landau's only mistake)
9. Hamiltonian dynamics I: failure of perturbation analysis for strong nonlinearity; KAM tori
10. Hamiltonian dynamics II: fate of destroyed tori; Poincare's big question answered; gaps in the asteroid belt
11. Hamiltonian dynamics III: Arnold's cat; Smale horseshoe; symbolic dynamics and Riverside Geyser
12. Chaos in open systems: transients and repellors; chaotic scattering
13. Selected topics: choice from quantum chaos, catastrophe theory, self-organized criticality, etc.
14. Student project presentations

Prerequisites
Mathematics through ordinary differential equations. Familiarity with classical mechanics helpful. Consult instructor for more information.

Instructor
John Sommerer is Director of the Milton S. Eisenhower Research and Technology Development Center at the Johns Hopkins  University Applied Physics Laboratory. Dr. Sommerer has done theoretical and experimental research in nonlinear dynamics that has been featured on the covers of both Science and Nature.

E-mail the instructor.

Course Section, Location, and Time

Computer Lab Requirements
Student homework and projects typically require use of software provided with textbook (and available on Kossiakoff Education Center workstations for students without other access to personal computers). No specific laboratories are required.

Textbooks
DYNAMICS: Numerical Explorations (2nd ed.) by H.E. Nusse, James A. Yorke

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Applied Physics

updated November 1998