Results 121 to 130 of about 152 (152)
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Symplectic Submanifolds and Symplectic Ideals
Journal of Lie Theory, 2006The purpose of the paper under review is to describe a method of studying symplectic submanifolds of Poisson manifolds by using the so-called symplectic ideals. Specifically, let \(N\) be a Poisson manifold. For every \(x\in N\) denote \({\mathfrak m}_x=\{f\in C^\infty(N)\mid f(x)=0\}\) and for every \(Q\subseteq C^\infty(N)\) set \({\mathcal V}(Q)=\{y\
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Mathematics of the USSR-Sbornik, 1970
Summary: In the article, the method of spherical reconstructions of smooth manifolds is applied to the computation of some groups of symplectic cobordisms. Namely, it is proved that \(\Omega^5_{Sp} = \mathbb Z_2\), \(\Omega^6_{Sp} = \mathbb Z_2\) and \(\Omega^7_{Sp} = 0\).
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Summary: In the article, the method of spherical reconstructions of smooth manifolds is applied to the computation of some groups of symplectic cobordisms. Namely, it is proved that \(\Omega^5_{Sp} = \mathbb Z_2\), \(\Omega^6_{Sp} = \mathbb Z_2\) and \(\Omega^7_{Sp} = 0\).
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Symplectic completion of symplectic jets
Journal of Mathematical Physics, 1996In this paper, we outline a method for symplectic integration of three degree-of-freedom Hamiltonian systems. We start by representing the Hamiltonian system as a symplectic map. This map (in general) has an infinite Taylor series. In practice, we can compute only a finite number of terms in this series. This gives rise to a truncated map approximation
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Symplectic Relations on Symplectic Manifolds
2011In this chapter we examine the notion of “relation” in the presence of a symplectic structure. To continue with the study of the relations between symplectic manifolds, we begin with the simplest but fundamental case of linear relations between symplectic vector spaces.
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The Quarterly Journal of Mathematics, 1993
Let \(Z\) be a real vector space with algebraic dual \(Z^*\) and on the direct sum \(V_z= Z\oplus Z^*\) define \(\Omega_z (x\oplus \xi, y\oplus \eta)= \xi(y)- \eta (x)\), for \(x,y\in Z\) and \(\xi, \eta\in Z^*\). The author shows here that the real symplectic vector space \((V_z, \Omega_z)\) given by infinite-dimensional \(Z\) has a variety of ...
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Let \(Z\) be a real vector space with algebraic dual \(Z^*\) and on the direct sum \(V_z= Z\oplus Z^*\) define \(\Omega_z (x\oplus \xi, y\oplus \eta)= \xi(y)- \eta (x)\), for \(x,y\in Z\) and \(\xi, \eta\in Z^*\). The author shows here that the real symplectic vector space \((V_z, \Omega_z)\) given by infinite-dimensional \(Z\) has a variety of ...
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Associated symplectic and co-symplectic structures
International Journal of Theoretical Physics, 1991Authors' introduction: ``Recently the authors [Int. J. Theor. Phys. 29, No. 1, 57--73 (1990; Zbl 0698.53020)] introduced a new geometrical structure, called cosymplectic structure. This structure, which is based on a symmetric bilinear form of signature zero, leads to a geometry that is in many respects analogous to the symplectic geometry.
Frescura, F. A. M., Lubczonok, G.
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Thoughts on Symplectic Groups and Symplectic Equations
2004Symplectic groups are characterized by their subdegrees. Symplectic equations are recognized by symplectic forms. Odd dimensional orthogonal groups in characteristic two are recognized by modified vectorial derivatives. Orbitcounting lemma and its consequences are reviewed.
Shreeram S. Abhyankar +1 more
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SYMPLECTIC COBORDISM WITH SINGULARITIES
Mathematics of the USSR-Izvestiya, 1984Translation from Izv. Akad. Nauk SSSR, Ser. Mat. 47, No.2, 230-247 (1983; Zbl 0531.55004).
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