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Hamiltonian systems, symplectic flows, classical integrable systems

1 vote
1 answer
326 views

Is a homogeneous symplectic isotopy always Hamiltonian?

The following statements are written in the Guillermou-Kashiwara-Shapira's paper "Sheaf quantization of Hamiltonian isotopies and applications to non-displaceability". Let $M$ be a smooth manifold an …
3 votes
1 answer
196 views

Any homogeneous symplectomorphism of cotangent bundle $\dot{T}^*M=T^*M-0_M$ preserves the ca...

Let $\phi$ be a homogeneous symplectomorphism of tangent bundle $\dot{T}^*M=T^*M-0_M$ and let $\alpha_M$ be the canonical Liouville 1-form of $\dot{T}^*M$. Then is it true that $\phi^*\alpha_M=\alpha_ …
1 vote
0 answers
78 views

Lifting of Contact isotopies on a symplectization

Let $\mathbb{R}^{2n}\times\mathbb{R}=\mathbb{R}^n\times\mathbb{R}^n\times\mathbb{R}=\{(q,p,z)|{q},{p}\in\mathbb{R}^n,z\in\mathbb{R}\}$ be a contact manifold with the standard contact form $\alpha=pdq+ …