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Questions tagged [symplectic-geometry]

Symplectic geometry is a branch of differential geometry and differential topology which studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form.

Symplectic geometry is a branch of differential geometry and differential topology which studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry has its origins in the Hamiltonian formulation of classical mechanics where the phase space of certain classical systems takes on the structure of a symplectic manifold. For more information please consult the Wikipedia page on symplectic geometry.

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Two functions generate the same lagrangian submanifold if and only if they differ by a locally constant function

From the book: Symplectic Geometry by Ana Cannas da Silva, page 19. The following statement is claimed, but I don't full understand it, neither know how to prove it on my own. Two functions generate the same lagrangian submanifold if and only if…
user161851
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Symplectic standard form

By reading an introduction to symplectic geometry the author of the text said that the standard symplectic form $w_0 = \sum_{j=1}^{n} dx_j \wedge dy_j$ on $\mathbb{R}^{2n}$ equals the form $w = \frac{i}{2} \sum_{j=1}^{n} dz_j \wedge d\bar{z}_j$ on…
Donut
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Looking for topics in symplectic geometry suitable for a 1 hour talk

I am a master2 student and I am looking for a topic in symplectic geometry to make a 1 hour presentation with. I only had a short introduction course to symplectic geometry so subjects shouldn't be too advanced. It could be the proof of a nice…
Thalanza
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Cartesian product of $\mathbb{S}^1$ is symplectic

Prove that the Cartesian products of $\mathbb{S}^1$ for $2n$ times is a symplectic manifold. I have just studied the concepts of symplectic manifold in the class of analytical mechanics. I have not studied any courses about geometry. So I want to…
Li Li
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symplectic sructure on a ball

We know by Darboux theorem that any symplectic form on a manifold $W^{2n}$ is locally symplectomorophic to the standard symplectic form $dx\wedge dy$ on $R^{2n}$. Is it true that any symplectic form on a ball $B^{2n}$ of arbitrary radius is…
7779052
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Question about image point Hamiltonian function

Are all points in the image of a Hamiltonian function regular value, Why? If not, is 0 a regular value?
Grey
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