Product Description

Winner of the 1998 Ferran Sunyer i Balaguer Prize

This book is devoted to the relation between two different concepts of integrability: the complete integrability of complex analytical Hamiltonian systems and the integrability of complex analytical linear differential equations. In addition to the theory, the book also presents several important applications, including homogeneous potentials, Bianchi IX cosmological model, three-body problem, Hnon-Heiles system, etc. The book is based on the original joint research of the author with J.M. Peris, J.P. Ramis and C. Sim, but an effort was made to present these achievements in their logical order rather than their historical one. The necessary background on differential Galois theory and Hamiltonian systems is included, and several new problems and conjectures which open new lines of research are proposed.

Series: Progress in Mathematics, Vol. 179

Product Details

• Amazon Sales Rank: #182007 in eBooks
• Published on: 1999-07-31
• Format: Kindle Book
• Number of items: 1

Review
"...[an] account of recent work of the author and co-workers on obstructions to the complete integrability of complex Hamiltonian systems. The methods are of considerable importance to practitioners... The book provides all the needed background...and presents concrete examples in considerable detail... The final chapter...includes a fascinating account of work-in-progress by the author and his collaborators... Of particular interest...is the program of extending the differential Galois theory to higher-order variational equations... [an] excellent introduction to non-integrability methods in Hamiltonian mechanics [that] brings the reader to the forefront of research in the area. The inclusion of a large number of worked-out examples, many of wide applied interest, is commendable. There are many historical references, and an extensive bibliography." --Mathematical Reviews