MSI Weekly Bulletin - Week starting Monday 12 March, 2007

The Chaos Game is a type of Markov Chain Monte Carlo algorithm applied to computing attractors and invariant measures associated with diverse fractal objects. This talk will pick on exciting aspects and applications of the Chaos Game, and the underlying ergodic theorem which it exploits, including restless textures, anti-aliasing, coupled IFS, fractal homeomorphisms, Bezier curves and splines, approximation of smooth functions by rough ones, and the "Kigami triangle". BIO: http://wwwmaths.anu.edu.au/~barnsley/

Anyone interested or possibly interested in participating in the algebra seminar this semester, please come to this brief organisational meeting, especially if you want to volunteer to speak or to suggest a speaker.

This Colloquium will be interesting to students, from undergrad to retiree, who know basic calculus and Hamiltonian mechanics. I shall review aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together the two major threads of its early development: celestial mechanics and control theory, and focussing on qualitative theory. From this perspective I show how concepts of stability enable us to classify dynamical equations and their solutions and connect the key issues of nonlinearity, bifurcation, control, and uncertainty that are common to time-dependent problems in natural and engineered systems. I shall discuss stability and bifurcations in a few simple model problems, and a recent extension of stability theory to complex networks.