Titlebook: Differential Geometry and Mathematical Physics; Part I. Manifolds, L Gerd Rudolph,Matthias Schmidt Book 2013 Springer Science+Business Medi

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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

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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. ..

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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

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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.

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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.

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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

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