This book has its origin in a lecture series hosted by the Federal University of Pernambuco in Recife, Brazil, between 1993 and 1999. Immediately after opening the book, one gets a feeling of the great enthusiasm of its editors, organizers of the corresponding series of lectures. It is a really attractive book, presenting many important topics from Hamiltonian dynamics and celestial mechanics in an accessible way. The editors and the mathematical centre in the equator, colonial city of Recife, deserve great admiration for producing such an impressive output - a record of their long term seminar, devoted to classical mechanics. (Several contributions to the seminar were published independently, before the publication of this book.) The book contains the following contributions: Central configurations and relative equilibria for the N-body problem (by D. Schmidt), Singularities of the N-body problem (by F. Diacu), Lectures on the two-body problem (by A. Albouy), Normal forms of Hamilton systems and stability of equilibria (by H. E. Cabral), The Poincaré compactification and applications to celestial mechanics (by E. Pérez-Chavela), The motion of the moon (by D. Schmidt), Lectures on geometrical methods in mechanics (by M. Levi), Momentum maps and geometric phases: Overview, classical adiabatic angles, holonomy for gyrostats, microswimming (by J. Koiller et al.), and Bifurcation from families of periodic solutions (J. K. Hale and P. Táboas).

Reviewer:

mzah