Infinite Dimensional Dynamical Systems

​This collection covers a wide range of topics of infinite

dimensional dynamical systems generated by parabolic partial differential

equations, hyperbolic partial differential equations, solitary equations,

lattice differential equations, delay differential equations, and stochastic

differential equations.

Infinite dimensional dynamical systems are generated by

evolutionary equations describing the evolutions in time of systems whose

status must be depicted in infinite dimensional phase spaces. Studying the

long-term behaviors of such systems is important in our understanding of their

spatiotemporal pattern formation and global continuation, and has been among

major sources of motivation and applications of new developments of nonlinear

analysis and other mathematical theories. Theories of the infinite dimensional

dynamical systems have also found more and more important applications in

physical, chemical, and life sciences.

This book collects 19 papers from 48 invited lecturers to

the International Conference on Infinite Dimensional Dynamical Systems held at

York University, Toronto, in September of 2008. As the conference was dedicated

to Professor George Sell from University of Minnesota on the occasion of his

70th birthday, this collection reflects the pioneering work and influence of

Professor Sell in a few core areas of dynamical systems, including

non-autonomous dynamical systems, skew-product flows, invariant manifolds

theory, infinite dimensional dynamical

systems, approximation dynamics, and fluid flows.​