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Titlebook: Differential Galois Theory and Non-Integrability of Hamiltonian Systems; Juan J. Morales Ruiz Book 1999 Springer Basel 1999 Dynamical Syst

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發(fā)表于 2025-3-21 17:38:30 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書(shū)目名稱(chēng)Differential Galois Theory and Non-Integrability of Hamiltonian Systems
編輯Juan J. Morales Ruiz
視頻videohttp://file.papertrans.cn/279/278722/278722.mp4
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
叢書(shū)名稱(chēng)Progress in Mathematics
圖書(shū)封面Titlebook: Differential Galois Theory and Non-Integrability of Hamiltonian Systems; Juan J. Morales Ruiz Book 1999 Springer Basel 1999 Dynamical Syst
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
關(guān)鍵詞Dynamical System; Galois group; Galois theory; algebra; differential algebra; differential equation; dynam
版次1
doihttps://doi.org/10.1007/978-3-0348-8718-2
isbn_softcover978-3-0348-0720-3
isbn_ebook978-3-0348-8718-2Series ISSN 0743-1643 Series E-ISSN 2296-505X
issn_series 0743-1643
copyrightSpringer Basel 1999
The information of publication is updating

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Progress in Mathematicshttp://image.papertrans.cn/d/image/278722.jpg
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Differential Galois Theory and Non-Integrability of Hamiltonian Systems978-3-0348-8718-2Series ISSN 0743-1643 Series E-ISSN 2296-505X
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Lipogenesis Pathway: Radiolabeled Choline,n and A and . are, in general, complex parameters. It is assumed, in what follows, that the roots of the polynomial . associated to . are simple (otherwise . is reduced to elementary functions). This is ensured if the discriminant.is non-zero, where g. and g. are the associated invariants (see Chapter 2).
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Laura Evangelista,Alessandra ZorzAfter the long preliminary work of Chapters 2 and 3, we now give the central theoretical results of this book. They will be used in a systematic way in the rest of this book.
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Introduction,During recent years the search for non-integrability criteria for Hamiltonian systems based upon the behaviour of solutions in the complex domain has acquired more and more relevance.
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Non-integrability Theorems,After the long preliminary work of Chapters 2 and 3, we now give the central theoretical results of this book. They will be used in a systematic way in the rest of this book.
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