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Differential Galois Theory and Non-Integrability of Hamiltonian Systems (Progress in Mathematics) [Hardcover]

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Item description for Differential Galois Theory and Non-Integrability of Hamiltonian Systems (Progress in Mathematics) by Juan J. Morales Ruiz...

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. For linear differential equations, integrability is made precise within the framework of differential Galois theory. The connection of these two integrability notions is given by the variational equation (i.e. linearized equation) along a particular integral curve of the Hamiltonian system. The underlying heuristic idea, which motivated the main results presented in this monograph, is that a necessary condition for the integrability of a Hamiltonian system is the integrability of the variational equation along any of its particular integral curves. This idea led to the algebraic non-integrability criteria for Hamiltonian systems. These criteria can be considered as generalizations of classical non-integrability results by Poincar and Liapunov, as well as more recent results by Ziglin and Yoshida. Thus, by means of the differential Galois theory it is not only possible to understand all these approaches in a unified way but also to improve them. Several important applications are also included: 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.





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Item Specifications...


Pages   168
Est. Packaging Dimensions:   Length: 9.2" Width: 6.2" Height: 0.6"
Weight:   0.9 lbs.
Binding  Hardcover
Release Date   Sep 24, 1999
Publisher   Birkhäuser Basel
ISBN  376436078X  
ISBN13  9783764360788  


Availability  0 units.


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1Books > Special Features > New & Used Textbooks > Sciences > Mathematics > Algebra & Trigonometry
2Books > Subjects > Professional & Technical > Professional Science > Mathematics > Geometry & Topology > Topology
3Books > Subjects > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Algebra > Abstract
4Books > Subjects > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Functional Analysis
5Books > Subjects > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Group Theory
6Books > Subjects > Science > General
7Books > Subjects > Science > Mathematics > General
8Books > Subjects > Science > Mathematics > Geometry & Topology > Topology
9Books > Subjects > Science > Mathematics > Pure Mathematics > Algebra > Abstract
10Books > Subjects > Science > Mathematics > Pure Mathematics > Algebra > General
11Books > Subjects > Science > Mathematics > Pure Mathematics > Calculus
12Books > Subjects > Science > Mathematics > Pure Mathematics > Functional Analysis
13Books > Subjects > Science > Mathematics > Pure Mathematics > Group Theory



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