Titlebook: Algebraic Integrability, Painlevé Geometry and Lie Algebras; Mark Adler,Pierre Moerbeke,Pol Vanhaecke Book 2004 Springer-Verlag Berlin Hei

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书目名称Algebraic Integrability, Painlevé Geometry and Lie Algebras影响因子(影响力)




书目名称Algebraic Integrability, Painlevé Geometry and Lie Algebras影响因子(影响力)学科排名




书目名称Algebraic Integrability, Painlevé Geometry and Lie Algebras网络公开度




书目名称Algebraic Integrability, Painlevé Geometry and Lie Algebras网络公开度学科排名




书目名称Algebraic Integrability, Painlevé Geometry and Lie Algebras被引频次




书目名称Algebraic Integrability, Painlevé Geometry and Lie Algebras被引频次学科排名




书目名称Algebraic Integrability, Painlevé Geometry and Lie Algebras年度引用




书目名称Algebraic Integrability, Painlevé Geometry and Lie Algebras年度引用学科排名




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失望未来

Lie Algebrasll be used. Since algebraic geometry, mainly the geometry of Abelian varieties, will only show up later and since we will need to do in that case a little more than just a review, we defer that subject to Part II of the book.

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Poisson Manifoldsnctions on .. and (.., ..., .., .. ..., ..) are linear coordinates on ... He observed that if . and . are two first integrals of a mechanical system (defined on ..) then their . {.} is also a first integral. Notice that the Poisson bracket also allows one to describe the equations of motion in their

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overhaul

出来

A.c.i. Systemsex) momentum map is the best possible complex analogue of the geometry that appears in the Liouville Theorem (Theorem 4.28). Namely, in many relevant examples the generic complexified fiber is an affine part of an . (a compact algebraic torus, see Chapter 5) and the integrable vector fields are tran

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顽固

Periodic Toda Lattices Associated to Cartan Matricesone, {.., ..} = {.., ..} = 0 and {.., ..} = .., where 1 ≤ . ≤ .. For a mechanical interpretation, consider . unit mass particles on a circle that are connected by exponential springs. In [33], Bogoyavlensky proposed a Lie algebraic generalization, where the original Toda lattice corresponds to the r

Musket

An Invitation to Deep Active Learninglid in the real case. For a complex version of the Liouville Theorem, we refer to Section 6.3. Lax equations, which often represent a vector field of an integrable system, are the subject of Sections 4.4 and 4.5.

construct

Deep Belief Nets in C++ and CUDA C: Volume 2slation invariant, when restricted to any of these tori. Such integrable systems are the main topic of this book, and we will call them algebraic completely integrable systems, following the original definition of Adler and van Moerbeke (see [14]).