Local symplectic algebra of quasi-homogeneous curves
نویسندگان
چکیده
منابع مشابه
Local Symplectic Algebra of Quasi-homogeneous Curves
We study the local symplectic algebra of parameterized curves introduced by V. I. Arnold in [A1]. We use the method of algebraic restrictions to classify symplectic singularities of quasi-homogeneous curves. We prove that the space of algebraic restrictions of closed 2-forms to the germ of a K-analytic curve is a finite dimensional vector space. We also show that the action of local diffeomorph...
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We study the local symplectic algebra of parameterized curves introduced by V. I. Arnold in [A1]. We use the method of algebraic restrictions to classify symplectic singularities of quasi-homogeneous curves. We prove that the space of algebraic restrictions of closed 2-forms to the germ of a quasihomogeneous curve is a finite dimensional vector space. We also show that the action of local diffe...
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To the best of our knowledge, the study of the local symplectic invariants of submanifolds of Euclidean space was initiated by Chern and Wang in 1947, [6]. They considered mainly the case of curves and hypersurfaces, and obtained structure equations defining a set of local symplectic differential invariants for these objects. We should explain at this stage that by “symplectic invariants” we me...
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We study the behavior of conformally symplectic systems near rotational Lagrangian tori. We recall that conformally symplectic systems appear for example in mechanical models including a friction proportional to the velocity. We show that in a neighborhood of these quasi–periodic solutions (either transitive tori of maximal dimension or periodic solutions), one can always find a smooth symplect...
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Let k be an algebraically closed field of characteristic 0, and let A = k[x, y]/(f) be a quasi-homogeneous plane curve. We show that for any graded torsion free A-module M without free summands, there exists a natural graded integrable connection, i.e. a graded A-linear homomorphism ∇ : Derk(A) → Endk(M) that satisfy the derivation property and preserves the Lie product. In particular, a torsio...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2009
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm204-1-4