Nonlinear Phenomena and Complex Systems

This book contains the lectures given at the II Canference an Dynamics and Randamness held at the Centro de Modelamiento Matematico of the Universidad de Chile, from December 9th to 13th, 2002. This meeting brought together mathematicians, theoretical physicists, theoretical computer scientists, and graduate students interested in fields related to probability theory, ergodic theory, symbolic and topological dynamics. We would like to express our gratitude to an the participants of the conference and to the people who contributed to its orga­ nization. In particular, to Pierre Collet, BerIiard Rost and Karl Petersen for their scientific advise. We want to thank warmly the authors of each chapter for their stimulating lectures and for their manuscripts devoted to a various of appealing subjects in probability and dynamics: to Jean Bertoin for his course on Some aspects of random fragmentation in con­ tinuous time; to Anton Bovier for his course on Metastability and ageing in stochastic dynamics; to Steve Lalley for his course on AI­ gebraic systems of generat ing functions and return probabilities for random walks; to Elon Lindenstrauss for his course on Recurrent measures and measure rigidity; to Sylvie Meleard for her course on Stochastic particle approximations for two-dimensional N avier­ Stokes equations; and to Anatoly Vershik for his course on Random and universal metric spaces.