| 书目名称 | Differential Galois Theory and Non-Integrability of Hamiltonian Systems |
| 编辑 | Juan J. Morales Ruiz |
| 视频video | |
| 概述 | Award-winning monograph of the Ferran Sunyer i Balaguer Prize 1998.Well-balanced exposition addressing the relation between two different concepts of integrability.Proposes problems and conjectures wh |
| 丛书名称 | Progress in Mathematics |
| 图书封面 |  |
| 描述 | .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 i |
| 出版日期 | Book 1999 |
| 关键词 | Dynamical System; Galois group; Galois theory; algebra; differential algebra; differential equation; dynam |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-0348-8718-2 |
| isbn_softcover | 978-3-0348-0720-3 |
| isbn_ebook | 978-3-0348-8718-2Series ISSN 0743-1643 Series E-ISSN 2296-505X |
| issn_series | 0743-1643 |
| copyright | Springer Basel 1999 |
发表于 2025-3-21 17:38:30
