Alongi (mathematics and computer science, Pomona College) and Nelson (mathematics, Carleton College) seek, along with Poisson and generations after him, what it means for a solution of a differential equation to be recurrent. Their approach develops increasingly more general topological modes of recurrence for dynamic situations beginning with fixed points and concluding with chain recurrent points. They include extensive examples as they cover flows, recurrent points, irreducible sets and test functions. They also include appendices on discrete dynamical systems, circle rotations and the Hausdorff metric and a range of exercises for each chapter. Annotation ©2007 Book News, Inc., Portland, OR (booknews.com)