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Titlebook: Visual Geometry and Topology; Anatolij T. Fomenko Book 1994 Springer-Verlag Berlin Heidelberg 1994 Hamiltonian Systems.Hamiltonsche System

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发表于 2025-3-21 16:52:05 | 显示全部楼层 |阅读模式
书目名称Visual Geometry and Topology
编辑Anatolij T. Fomenko
视频video
图书封面Titlebook: Visual Geometry and Topology;  Anatolij T. Fomenko Book 1994 Springer-Verlag Berlin Heidelberg 1994 Hamiltonian Systems.Hamiltonsche System
描述Geometry and topology are strongly motivated by thevisualization of idealobjects that have certain specialcharacteristics. A clear formulation of a specific propertyor a logically consistent proof of a theorem oftencomesonly after the mathematician has correctly "seen" what isgoing on. These pictures which are meant to serve assignposts leading to mathematical understanding, frequentlyalso contain a beauty of their own.The principal aim of this book is to narrate, in anaccessible and fairly visual language, about some classicaland modern achievements of geometry and topology in bothintrinsic mathematical problems and applications tomathematical physics. The book starts from classicalnotionsof topology and ends with remarkable new results inHamiltonian geometry. Fomenko lays special emphasis uponvisual explanations of the problems and results anddownplays the abstract logical aspects ofcalculations. Asan example, readers can very quickly penetrate into thenewtheory of topological descriptions of integrableHamiltoniandifferential equations. The book includes numerousgraphicalsheets drawn by the author, which are presented inspecialsections of "Visual material". These pictures illustr
出版日期Book 1994
关键词Hamiltonian Systems; Hamiltonsche Systeme; Integrable Systems; Integrierbare Systeme; Visual Geometry; Vi
版次1
doihttps://doi.org/10.1007/978-3-642-76235-2
isbn_softcover978-3-642-76237-6
isbn_ebook978-3-642-76235-2
copyrightSpringer-Verlag Berlin Heidelberg 1994
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https://doi.org/10.1007/978-3-642-76235-2Hamiltonian Systems; Hamiltonsche Systeme; Integrable Systems; Integrierbare Systeme; Visual Geometry; Vi
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Low-Dimensional Manifolds,bone of the whole building is the .. On lower storeys, it is at first local, i.e. events occur in a small enough domain of a manifold. Ascending, the theory develops global aspects and finally, on the top, the modern geometry operates with essentially nonlocal effects.
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Visual Symplectic Topology and Visual Hamiltonian Mechanics,vides a good deal of qualitative information on the behaviour of certain physical systems. Among the variety of mechanical and physical systems there exists an important class described using so-called Hamiltonian equations. These systems can be realized on even-dimensional manifolds only.
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Low-Dimensional Manifolds,f differential geometry exhibits two basic layers. The one which was historically the first to appear may be conditionally called . which usually develops in a region of a Euclidean space. This is the foundation and the first storeys of the whole edifice. Then there appeared next storeys which took
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Visual Symplectic Topology and Visual Hamiltonian Mechanics, ≤ . ≤ . and .(.,..., .) are smooth functions which are components of the field .. Thus, each vector field is interpreted as a system of ordinary differential equations on a manifold. Inversely, each system or ordinary differential equations can be represented as the vector field on a corresponding
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