附註:Papers from a conference held Apr. 28-May 2, 1997, in Bremen, Germany.
Includes bibliographical references and index.
Stability along trajectories at a stochastic bifurcation point / Peter Baxendale -- Bifurcations of one-dimensional stochastic differential equations / Hans Crauel, Peter Imkeller, and Marcus Steinkamp -- P-bifurcations in the noisy duffing-van der Pol equation / Yan Liang and N. Sri Namachchivaya -- The stochastic Brusselator: parametric noise destroys Hopf bifurcation / Ludwig Arnold, Gabriele Bleckert, and Klaus Reiner Schenk-Hoppé -- Numerical approximation of random attractors / Hannes Keller and Gunter Ochs -- Random hyperbolic systems / Volker Matthias Gundlach and Yuri Kifer -- Some questions in random dynamical systems involving real noise processes / Russell Johnson -- Topological, smooth, and control techniques for perturbed systems / Fritz Colonius and Wolfgang Kliemann -- Perturbation methods for Lyapunov exponents / Volker Wihstutz -- The Lyapunov exponent of the Euler scheme for stochastic differential equations / Denis Talay -- Towards a theory of random numerical dynamics / Peter E. Kloeden, Hannes Keller and Björn Schmalfuss -- Canonical stochastic differential equations based on Lévy processes and their supports / Hiroshi Kunita -- On the link between fractional and stochastic calculus / Martina Zähle -- Asymptotic curvature for stochastic dynamical systems / Michael Cranston and Yves Le Jan -- Stochastic analysis on (infinite-dimensional) product manifolds / Sergio Albeverio, Alexei Daletskii, and Yuri Kondratiev -- Evolutionary dynamics in random environments / Lloyd Demetrius and Volker Matthias Gundlach -- Microscopic and mezoscopic models for mass distributions / Peter Kotelenez.
摘要:This volume gives an account of new and recent developments in the theory of random and, in particular, stochastic dynamical systems. Its purpose is to document and, to some extent, summarise the current state of the field of random dynamical systems beyond the recent monograph, "Random Dynamical Systems" by Ludwig Arnold. The book is intended for an audience of researchers and graduate students from stochastics as well as dynamics. It contains carefully refereed contributions from experts in the field, chosen such that a consistent picture can be given. Recent results on stochastic bifurcation, hyperbolic systems, numerics and asymptotics, more general driving processes for stochastic differential equations, and stochastic analysis on infinite-dimensional manifolds are presented in a comprehensible manner. Several new and exciting insights int o the unexpected variety of dynamical behaviours resulting from the influence of stochastic perturbations are conveyed to the reader.
