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Differential Galois Theory and Non-Integrability of Hamiltonian Systems by Juan J. Morales Ruiz (auth.) is a nonfiction available to read on EtoBox.

What is Differential Galois Theory and Non-Integrability of Hamiltonian Systems about?

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 Poincaré and Lyapunov, 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 im

Who reads Differential Galois Theory and Non-Integrability of Hamiltonian Systems?

Author

Juan J. Morales Ruiz (auth.)

Publisher

Birkhäuser Basel

Published

1999

Language

EN

ISBN

9783034807234

Category

nonfiction

Subjects

Mathematics, Stem