effective low-dimensional behavior in the transition to turbulence. The practical im-
plications for a low-dimensional description of complex global bifurcations in fluid
systems are especially promising. More generally the finite-dimensional behavior of
turbulent flows and the reduction of the number of determining modes is of great
The organizers wish to thank the National Science Foundation and the Air Force
Office for Scientific Research for their generous support. Also the Center for Nonlin-
ear Studies at Los Alamos National Laboratory provided valuable indirect support.
Finally, Ms. Betty Verducci and Carole Kohanski from the American Mathematical
Society deserve special recognition for their relentless efforts in making this Summer
Seminar successful.
Ciprian Foias
Basil Nicolaenko
Roger Temam
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