P605 | 3498 | J. Townsend

Our goal is to present some basic aspects of linear and non linear dynamics, at least at an introductory level. A sampling of likely topics are: first vs. higher order systems, linear vs. non linear systems, autonomous vs. non autonomous systems, phase space, topological equivalence of orbits and introduction to symbolic dynamics, bifurcation and catastrophe theory, definitions of chaos, Hamiltonian and gradient systems, various kinds of stability, an introduction to ergodic theory in 'deterministic' dynamic systems. Poincare' maps, fractal structures and dimension, difference vs. differential equations and maps vs. flows, Lyapunov exponents, strange attractors, diverse kinds of oscillators, Morse-Smale systems, Horse-shoe maps, averaging methods for non autonomous systems. The lectures will be tuned to the mathematics, but approached more as in physics as opposed to an axiomatic treatment. An occasional important proof may be given. And considerable effort will be made to make the mathematics intuitive to the extent possible and depending on the individual student's background. Extant and potential applications in cognitive science will be taken up, and I am eager to learn of new applications. If time is available, some effort will be expended on empirical data analysis, though that cannot dominate lecture sessions. Since it will probably turn out that variation of mathematical background in the audience will be large, I expect each student to learn at his/her own level, each striving to learn as much as possible at that particular stratum. The students will be encouraged to avail themselves of the wonderful and relatively inexpensive computer software for exploration of "dynamics country."