By Martin Golubitsky,Dan Luss,Steven H. Strogatz

This IMA quantity in arithmetic and its functions development FORMATION IN non-stop and paired platforms relies at the court cases of a workshop with an identical identify, yet is going be­ yond the complaints by means of providing a sequence of mini-review articles that sur­ vey, and supply an creation to, attention-grabbing difficulties within the box. The workshop used to be a vital part of the 1997-98 IMA software on "EMERG­ ING purposes OF DYNAMICAL SYSTEMS." i need to thank Martin Golubitsky, college of Houston (Math­ ematics) Dan Luss, collage of Houston (Chemical Engineering), and Steven H. Strogatz, Cornell college (Theoretical and utilized Mechan­ ics) for his or her first-class paintings as organizers of the assembly and for enhancing the complaints. I additionally take this chance to thank the nationwide technology origin (NSF), and the military learn place of work (ARO), whose monetary help made the workshop attainable. Willard Miller, Jr., Professor and Director v PREFACE development formation has been studied intensively for many of this cen­ tury via either experimentalists and theoreticians, and there were many workshops and meetings dedicated to the topic. within the IMA workshop on development Formation in non-stop and paired structures held may perhaps 11-15, 1998 we tried to target new instructions within the styles literature.

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