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Hamiltonian Systems
In this chapter we give the overviews of Lagrangian and Hamiltonian systems. The basics of Lagrangian and Hamiltonian mechanics, Hamiltonian flows in...
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Mahler’s conjecture for some hyperplane sections
We use symplectic techniques to obtain partial results on Mahler’s conjecture about the product of the volume of a convex body and the volume of its...
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50 Years of translation structures
In this paper the term translation structure will denote any geometric object canonically constructed from an elementary abelian group. Hence,...
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Hamiltonian Systems Theory
This chapter deals with the basic theory of Hamiltonian systems. After the definition of a Hamiltonian system and two examples from Mechanics we show...
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Feynman Integrals and Mirror Symmetry
In this text we describe various approaches to the computation of Feynman integrals. One approach uses toric geometry to derive differential...
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Gutzwiller’s semiclassical trace formula and Maslov-type index theory for symplectic paths
Gutzwiller’s famous semiclassical trace formula plays an important role in theoretical and experimental quantum mechanics with tremendous success. We...
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Forcing theory for transverse trajectories of surface homeomorphisms
This paper studies homeomorphisms of surfaces isotopic to the identity by means of purely topological methods and Brouwer theory. The main...
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Cooperstein’s Theory of Symplecta and Parapolar Spaces
B. Cooperstein gave a criterion that symplecta (convex polar subspaces) exist. That theory is developed here in the somewhat wider context of a...
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Constant Scalar Curvature Metrics on Toric Surfaces
The main result of the paper is an existence theorem for a constant scalar curvature Kahler metric on a toric surface, assuming the K-stability of...
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Composition with Smooth Maps
If f is a map ℝ n → ℝ m then a function u in ℝ m can be...
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Introduction to Group Actions in Symplectic and Complex Geometry
In this preparatory chapter certain basic results on differentiable manifolds are outlined. Standard references should include [Sp] and [War].
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Admissible wavelets on the Siegel domain of type one
Let Sp(n, R ) be the sympletic group, and let K n * be its maximal compact subgroup. Then G = Sp ( n , R )/ K n * can be realized as the Siegel domain of type...
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Molecular Dynamics Simulations: The Limits and Beyond
This article reviews the present state of Molecular Dynamics (MD) simulations and tries to give an outlook into future developments. First an...