Lennaert van Veen Department of Mathematical and Statistical Science, La Trobe University Periodic motion versus turbulent motion Thursday 23nd, March 14:05-14:55pm, Carslaw Building Room 375. The application of dynamical systems theory to fluid mechanics has been very successful in the area of low Reynolds number flow and transitions form regular to chaotic motion. The transition to weak turbulence in constraint flows like Rayleigh- Benard convection and von Karman swirling flow has been explained in terms of bifurcation theory. Developed turbulence, however, remains largely mysterious. Two obvious reasons are the intrinsic complexity and the large number of degrees of freedom that need to be taken into account in simulations. Recently, developements in scientific computation have brought turbulence just within reach of numerical dynamical systems analysis. I will present recent work with Shigeo Kida (Kyoto University) and Genta Kawahara (Osaka University) on unstable periodic solutions to the Navier-Stokes equation which coexist with turbulence. By studying the peiodic time series we can learn about aspects of turbulent dynamics such as its Lyapunov spectrum and the energy cascade. We believe this fresh approach to turbulence research opens the way to a better understanding of many open questions. Not everyone agrees, however, and this presentation has led to many a heated debate.