The N-Vortex Problem: Analytical Techniques, P.K. Newton, Springer-Verlag Applied Mathematical Sciences Vol 145 (2001)
The book is an introduction to current research on the N-vortex problem of fluid mechanics in the spirit of several works on N-body problems from celestial mechanics. My goal is to describe the Hamiltonian aspects of vortex dynamics so that graduate students and researchers can use the book as an entry point into the large and growing literature on integrable and nonintegrable vortex problems. By describing the N-vortex problem as a branch of dynamical systems theory in a way that the N-body problem of celestial mechanics is often presented, I have tried to keep my focus fairly narrow, but deeper than a broader literature survey would be. The field of vortex dynamics is lively and active, using techniques that have widespread applicability to many general problems in dynamics and modern applied mathematics. It is my belief that an extensive study of the N-vortex problem provides an ideal entry into the field of nonlinear dynamics that is physically relevant and mathematically rich.
Geometry, Mechanics, and Dynamics: Volume in Honor of the 60th Birthday of J.E. Marsden, Eds. P.K. Newton, P. Holmes, A. Weinstein, Springer-Verlag (2002)
Jerry Marsden was one of the world’s pre-eminent mechanicians and applied mathematicians. He passed away on September 21, 2010 after fighting a long battle with prostate cancer. In August of 2002 many of his friends and colleagues helped him celebrate his 60th birthday at a workshop entitled ‘Geometry, Mechanics, and Dynamics’, held at the Fields Institute for Research in the Mathematical Sciences of which he was the founding director. Beginning in 1999, we began soliciting articles that might be used as entry points by students interested in fields that have been shaped by Jerry’s work. At the same time, we hoped to give experts engrossed in their own technical niches an indication of the wonderful breadth and depth of their subject as a whole. This book is an outcome of those efforts.
