標(biāo)題: Titlebook: Differential Geometry and Mathematical Physics; Part I. Manifolds, L Gerd Rudolph,Matthias Schmidt Book 2013 Springer Science+Business Medi [打印本頁(yè)] 作者: 一再 時(shí)間: 2025-3-21 19:27
書目名稱Differential Geometry and Mathematical Physics影響因子(影響力)
書目名稱Differential Geometry and Mathematical Physics影響因子(影響力)學(xué)科排名
書目名稱Differential Geometry and Mathematical Physics網(wǎng)絡(luò)公開度
書目名稱Differential Geometry and Mathematical Physics網(wǎng)絡(luò)公開度學(xué)科排名
書目名稱Differential Geometry and Mathematical Physics被引頻次
書目名稱Differential Geometry and Mathematical Physics被引頻次學(xué)科排名
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書目名稱Differential Geometry and Mathematical Physics年度引用學(xué)科排名
書目名稱Differential Geometry and Mathematical Physics讀者反饋
書目名稱Differential Geometry and Mathematical Physics讀者反饋學(xué)科排名
作者: 骨 時(shí)間: 2025-3-21 22:54
Vector Bundles,n physical models may be viewed in a coordinate-free manner as sections of certain vector bundles. We start by observing that the tangent spaces of a manifold combine in a natural way into what is called the tangent bundle. By taking the properties of the tangent bundle as axioms, we arrive at the n作者: 緊張過(guò)度 時(shí)間: 2025-3-22 02:17
Vector Fields,gebra of smooth functions, discuss the notions of integral curve and flow, introduce the Lie derivative and give a brief account to time-dependent vector fields. Thereafter, we give an introduction to (geometric) distributions, i.e., subsets of the tangent bundle which are locally spanned by vector 作者: Felicitous 時(shí)間: 2025-3-22 07:23
Differential Forms,he theory of integration and the Stokes Theorem, as well as an introduction to de Rham cohomology. Next, we discuss elements of Riemannian geometry and Hodge duality. As an application, we show how classical Maxwell electrodynamics can be understood in a coordinate-free way using the language of dif作者: EWE 時(shí)間: 2025-3-22 10:41
Lie Groups,lassical groups. Thereafter, we discuss left-invariant vector fields, define the Lie algebra of a Lie group and construct the exponential mapping, which provides a local diffeomorphism between the group and its algebra. This proves useful both for the study of the local structure of Lie groups and f作者: Hemiparesis 時(shí)間: 2025-3-22 15:54
Lie Group Actions,fields of a special type, called Killing vector fields. We prove the Orbit Theorem, which states that the distribution spanned by the Killing vector fields is integrable and that its integral manifolds coincide with the connected components of the orbits of the action. This way, every orbit gets end作者: Hemiparesis 時(shí)間: 2025-3-22 20:37
Linear Symplectic Algebra,mplectic geometry provides the natural mathematical framework for the study of Hamiltonian systems. In this chapter, we present linear symplectic algebra. We start with a discussion of the elementary properties of symplectic vector spaces, the various types of their subspaces and linear symplectic r作者: amorphous 時(shí)間: 2025-3-22 22:30
Symplectic Geometry, are locally equivalent. Thus, in sharp contrast to the situation in Riemannian geometry, symplectic manifolds of the same dimension can at most differ globally. The second important observation is that a symplectic structure provides a duality between smooth functions and certain vector fields, cal作者: 厭倦嗎你 時(shí)間: 2025-3-23 01:32 作者: 移動(dòng) 時(shí)間: 2025-3-23 05:48 作者: Firefly 時(shí)間: 2025-3-23 10:43
Integrability,em and with a number of examples: the two-body problem, the two-centre problem, the top, the spherical pendulum and the Toda lattice. Thereafter, we analyse Lax pairs in the context of Hamiltonian systems on coadjoint orbits. In particular, we show that the Toda lattice can be understood in this fra作者: 爆炸 時(shí)間: 2025-3-23 16:25
Hamilton-Jacobi Theory,atical physics. On the one hand, it builds a bridge between classical mechanics and other branches of physics, in particular, optics. On the other hand, it yields a link between classical and quantum theory. We start with deriving the Hamilton-Jacobi equation and proving the classical Jacobi Theorem作者: 壯觀的游行 時(shí)間: 2025-3-23 22:04 作者: Redundant 時(shí)間: 2025-3-23 23:23
https://doi.org/10.1007/978-94-007-5345-7Analysis on Manifolds; Differential Geometry Applied; Hamilton-Jacobi Theory; Hamiltonian Systems; Integ作者: Ccu106 時(shí)間: 2025-3-24 04:24
978-94-017-8198-5Springer Science+Business Media Dordrecht 2013作者: 干涉 時(shí)間: 2025-3-24 09:34 作者: ALLAY 時(shí)間: 2025-3-24 13:18 作者: 不吉祥的女人 時(shí)間: 2025-3-24 17:30
David Ben-Chaim,Yaffa Keret,Bat-Sheva Ilanys and discuss level sets in some detail. Thereafter, we carry over the concepts of differentiable mapping, tangent space and derivative from classical calculus to manifolds and derive manifold versions of the Inverse Mapping Theorem, the Implicit Mapping Theorem and the Constant Rank Theorem. Next, 作者: Ledger 時(shí)間: 2025-3-24 22:40 作者: GEN 時(shí)間: 2025-3-25 00:33 作者: 靦腆 時(shí)間: 2025-3-25 03:44
Three-Dimensional Approximationhe theory of integration and the Stokes Theorem, as well as an introduction to de Rham cohomology. Next, we discuss elements of Riemannian geometry and Hodge duality. As an application, we show how classical Maxwell electrodynamics can be understood in a coordinate-free way using the language of dif作者: 我怕被刺穿 時(shí)間: 2025-3-25 08:34
Three-Dimensional Approximationlassical groups. Thereafter, we discuss left-invariant vector fields, define the Lie algebra of a Lie group and construct the exponential mapping, which provides a local diffeomorphism between the group and its algebra. This proves useful both for the study of the local structure of Lie groups and f作者: 失望昨天 時(shí)間: 2025-3-25 13:27
A New View of Scientific Rationalityfields of a special type, called Killing vector fields. We prove the Orbit Theorem, which states that the distribution spanned by the Killing vector fields is integrable and that its integral manifolds coincide with the connected components of the orbits of the action. This way, every orbit gets end作者: iodides 時(shí)間: 2025-3-25 17:57
Methodology, Heuristics, and Rationalitymplectic geometry provides the natural mathematical framework for the study of Hamiltonian systems. In this chapter, we present linear symplectic algebra. We start with a discussion of the elementary properties of symplectic vector spaces, the various types of their subspaces and linear symplectic r作者: Headstrong 時(shí)間: 2025-3-25 22:05
https://doi.org/10.1007/978-1-349-14936-0 are locally equivalent. Thus, in sharp contrast to the situation in Riemannian geometry, symplectic manifolds of the same dimension can at most differ globally. The second important observation is that a symplectic structure provides a duality between smooth functions and certain vector fields, cal作者: 冰雹 時(shí)間: 2025-3-26 00:12 作者: 軍械庫(kù) 時(shí)間: 2025-3-26 07:57 作者: 秘密會(huì)議 時(shí)間: 2025-3-26 09:45 作者: Expediency 時(shí)間: 2025-3-26 12:55
On Non-Welfarist Social Ordering Functionsatical physics. On the one hand, it builds a bridge between classical mechanics and other branches of physics, in particular, optics. On the other hand, it yields a link between classical and quantum theory. We start with deriving the Hamilton-Jacobi equation and proving the classical Jacobi Theorem作者: 戲服 時(shí)間: 2025-3-26 20:06 作者: CHASM 時(shí)間: 2025-3-26 21:36
1864-5879 geometry for theoretical physicists.Prepares the reader to a.Starting from an undergraduate level, this book systematically develops the basics of.? .Calculus on manifolds, vector bundles, vector fields and differential forms,.? .Lie groups and Lie group actions,.? .Linear symplectic algebra and sym作者: 聲音刺耳 時(shí)間: 2025-3-27 04:55 作者: 高度贊揚(yáng) 時(shí)間: 2025-3-27 06:50
Linear Symplectic Algebra,ndex. These are homotopy invariants which contain information on how the members of a 1-parameter family of Lagrangian subspaces intersect a given Lagrangian subspace. They will play an essential role in the study of geometric asymptotics in Chap.?..作者: 1FAWN 時(shí)間: 2025-3-27 13:27
Book 2013ferential forms,.? .Lie groups and Lie group actions,.? .Linear symplectic algebra and symplectic geometry,.? .Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory..The topics listed under the first item are relevant for virtually all areas of mathematical phy作者: membrane 時(shí)間: 2025-3-27 17:38
David Ben-Chaim,Yaffa Keret,Bat-Sheva Ilanyl (or weakly embedded) submanifolds. Besides that, we derive criteria for a subset to admit a submanifold structure. Finally, we prove the Transversal Mapping Theorem, which states that the preimage of a submanifold under a differentiable mapping is again a submanifold, provided the mapping is transversal to that submanifold.作者: Foment 時(shí)間: 2025-3-27 21:41
Differentiable Manifolds,l (or weakly embedded) submanifolds. Besides that, we derive criteria for a subset to admit a submanifold structure. Finally, we prove the Transversal Mapping Theorem, which states that the preimage of a submanifold under a differentiable mapping is again a submanifold, provided the mapping is transversal to that submanifold.作者: 根除 時(shí)間: 2025-3-28 00:02 作者: 戲法 時(shí)間: 2025-3-28 04:10 作者: considerable 時(shí)間: 2025-3-28 09:28
Rational Bases and Generalized Barycentricsuce characteristic exponents and multipliers and construct Poincaré mappings. Next, we study elementary aspects of orbital stability: linear stability, stability in the hyperbolic case and Lyapunov functions. Finally, we construct the stable and the unstable manifolds of a critical integral curve an作者: degradation 時(shí)間: 2025-3-28 11:16 作者: dissent 時(shí)間: 2025-3-28 15:30
A New View of Scientific Rationalityan important special case, we discuss free proper actions and related bundle structures. In the final two sections, we study invariant vector fields and make some elementary remarks on relative equilibria and relatively periodic integral curves. This is relevant for the study of Hamiltonian systems 作者: fatty-streak 時(shí)間: 2025-3-28 20:21 作者: 摘要記錄 時(shí)間: 2025-3-29 02:51
https://doi.org/10.1007/978-1-349-14936-0n elliptic fixed point and for the Hamiltonian of a system near an equilibrium. The normal form of the Hamiltonian induces a foliation of the phase space into invariant tori so that, in the normal form approximation, the theory becomes integrable. Moreover, we prove the Birkhoff-Lewis Theorem, which作者: 疏遠(yuǎn)天際 時(shí)間: 2025-3-29 03:20
https://doi.org/10.1007/978-1-349-14936-0n the three-sphere, the Kepler problem (including the Moser regularization), the Euler top, the spherical pendulum and a model of gauge theory, which can be viewed as obtained from an approximation of gauge theory on a finite lattice. Finally, we give an introduction to the study of qualitative dyna
