Optimal Control and Geometry: Integrable Systems, Jurdjevic

Автор: N. J. Hitchin
Название: Integrable Systems
ISBN: 0199676771 ISBN-13(EAN): 9780199676774
Издательство: Oxford Academ
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Описание: Designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors, this book has its origins in a lecture series given by the internationally renowned authors. Written in an accessible, informal style, it fills a gap in the existing literature.

Автор: Yuri Fedorov; Valerij Vasilievich Kozlov
Название: A Memoir on Integrable Systems
ISBN: 3540590005 ISBN-13(EAN): 9783540590002
Издательство: Springer
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Описание: This book considers the larger class of systems which are not (at least a priori) Hamiltonian but possess tensor invariants, in particular, an invariant measure.

Автор: Gerdjikov Vladimir
Название: Integrable Hamiltonian Hierarchies
ISBN: 3642095771 ISBN-13(EAN): 9783642095771
Издательство: Springer
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Описание: This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their hierarchies.

Автор: Bolsinov
Название: Geometry and Dynamics of Integrable Systems
ISBN: 3319335022 ISBN-13(EAN): 9783319335025
Издательство: Springer
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Описание: Based on lectures given at an advanced course on integrable systems at the Centre de Recerca Matem?tica in Barcelona, these lecture notes address three major aspects of integrable systems: obstructions to integrability from differential Galois theory; the description of singularities of integrable systems on the basis of their relation to bi-Hamiltonian systems; and the generalization of integrable systems to the non-Hamiltonian settings. All three sections were written by top experts in their respective fields. Native to actual problem-solving challenges in mechanics, the topic of integrable systems is currently at the crossroads of several disciplines in pure and applied mathematics, and also has important interactions with physics. The study of integrable systems also actively employs methods from differential geometry. Moreover, it is extremely important in symplectic geometry and Hamiltonian dynamics, and has strong correlations with mathematical physics, Lie theory and algebraic geometry (including mirror symmetry). As such, the book will appeal to experts with a wide range of backgrounds.