UK Nonlinear News , August 1997.

Celestial Mechanics. The origin of Chaos and Stability

Florin Diacu & Philip Holmes

Princeton University Press

Reviewed by D. Knapp

For over two hundred years scientists have been confident that planetary motion is accurately modelled by a set of particles interacting through forces of mutual gravitational attraction. Although careful calculations allow accurate predictions of motion over small time periods there are subtle problems concerning the qualitative behaviour of solutions into the distant future which require more elaborate theoretical tools.

This book is a popular account of these tools and how they evolved, together with some biographical detail about the scientists and mathematicians who created them.

The book is very well written with difficult concepts sketched with great clarity. It is suitable for anyone whose background in mathematics included some differential equation theory and a little mechanics. It could be read by professional mathematicians to gain a rapid and stimulating overview of an old subject which now employs many of the mathematical concepts discovered this century.

The authors are ambitious, attempting to convey the concept of a homoclinic tangle and the subtlety of KAM theory. Although they can only be successful to a limited extent these sections convey the demanding nature of these highlights of mathematics well. This text deserves purchase by any library which wishes to help general readers keep abreast of the rapidly expanding frontier of mechanics.

D. Knapp, Department of Applied Mathematics, Leeds University.
email: amt6dk@amsta.leeds.ac.uk.



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