Memoirs of the American Mathematical Society 2009; 97 pp; softcover Volume: 198 ISBN10: 0821842641 ISBN13: 9780821842645 List Price: US$69 Individual Members: US$41.40 Institutional Members: US$55.20 Order Code: MEMO/198/925
 The authors study semilinear parabolic systems on the full space \({\mathbb R}^n\) that admit a family of exponentially decaying pulselike steady states obtained via translations. The multipulse solutions under consideration look like the sum of infinitely many such pulses which are well separated. They prove a global centermanifold reduction theorem for the temporal evolution of such multipulse solutions and show that the dynamics of these solutions can be described by an infinite system of ODEs for the positions of the pulses. As an application of the developed theory, The authors verify the existence of SinaiBunimovich spacetime chaos in 1D spacetime periodically forced SwiftHohenberg equation. Table of Contents  Introduction
 Assumptions and preliminaries
 Weighted Sobolev spaces and regularity of solutions
 The multipulse manifold: general structure
 The multipulse manifold: projectors and tangent spaces
 The multipulse manifold: differential equations and the cut off procedure
 Slow evolution of multipulse profiles: linear case
 Slow evolution of multipulse structures: center manifold reduction
 Hyperbolicity and stability
 Multipulse evolution equations: asymptotic expansions
 An application: spatiotemporal chaos in periodically perturbed SwiftHohenberg equation
 Bibliography
 Nomenclature
