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Symplectic vector space
About: Symplectic vector space is a research topic. Over the lifetime, 2048 publications have been published within this topic receiving 53456 citations.
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TL;DR: In this paper, it was shown that two simple, closed, real-analytic arcs in C2n that are polynomially convex are equivalent under the group of symplectic holomorphic automorphisms of C 2n if and only if the two arcs have the same action integral.
Abstract: We prove that two simple, closed, real-analytic curves in C2n that are polynomially convex are equivalent under the group of symplectic holomorphic automorphisms of C2n if and only if the two curves have the same action integral. Every two simple real-analytic arcs in C2n are so equivalent.
14 citations
TL;DR: In this paper, the definiteness of the discrete discrete symplectic system is characterized and a sufficient condition for the existence of densely defined operators associated with the system is provided. And the minimal and maximal linear relations associated with these systems are introduced.
14 citations
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TL;DR: In this article, the canonical involution of a double tangent bundle may be dualized in different ways to yield relations between the Tulczyjew diffeomorphism, the Poisson anchor associated with the standard symplectic structure on the cotangent space, and the reversal diff eomorphism.
Abstract: The canonical involution of a double (=iterated) tangent bundle may be dualized in different ways to yield relations between the Tulczyjew diffeomorphism, the Poisson anchor associated with the standard symplectic structure on the cotangent space,and the reversal diffeomorphism. We show that the constructions which yield these maps extend very generally to the double Lie algebroids of double Lie groupoids, where they play a crucial role in the relations between double Lie algebroids and Lie bialgebroids.
14 citations
01 Jan 1995
TL;DR: In this paper, it was shown that there exists a deep relationship between the differential topology of S 2-knots in ℝ4 and their symplectic geometry.
Abstract: We show in this paper that there exists a deep relationship between the differential topology of S 2-knots in ℝ4 and their symplectic geometry. In particular, we use symplectic tools to define a real-valued topological invariant of a knotted S 2 in ℝ4 (see Section 3.4 below). Here are the main results which motivate this definition.
14 citations
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TL;DR: In this paper, the authors studied isomorphism classes of symplectic dual pairs P P-, where P is an integrable Poisson manifold, S is symplectic, and the two maps are complete, surjective Poisson submersions with connected and simply-connected fibres.
Abstract: We study isomorphism classes of symplectic dual pairs P P-, where P is an integrable Poisson manifold, S is symplectic, and the two maps are complete, surjective Poisson submersions with connected and simply-connected fibres. For fixed P, these Morita self-equivalences of P form a group Pic(P) under a natural ``tensor product'' operation. We discuss this group in several examples and study variants of this construction for rings (the origin of the notion of Picard group), Lie groupoids, and symplectic groupoids.
14 citations