All Questions

Let $(M,\{.,.\})$ be a smooth Poisson manifold, and let $H\in C^\infty(M\times\mathbb{R},\mathbb{R})$. Question: Does there exist $H_0\in C^\infty(M,\mathbb{R})$ and smooth parameter-dependent Poisson ...

I'm stuck with the following claim made in Section 13.1 of Y-G. Oh's book "Symplectic topology and Floer homology". Assume that $N$ is a differential manifold and $S_0 ,S_1\subseteq N$ two ...

Assume $\mathcal{M}$ is a compact symplectic $2n$-dimensional manifold with a Hamiltonian action of the torus $\mathbb{T}^n$. Given a family of functions $F=(f_1,\ldots,f_n)$ defining an integrable ...

For a $n$ dimensional smooth manifold $M$, I consider the cotangent bundle $T^*M$ with the canonical symplectic form $\omega$. A symplectic map $\phi : T^*M \to T^* M$ is a map which leaves the ...

Given a $2n$-dimensional symplectic manifold $\mathcal{M}$ and two different lagrangian fibrations $\pi_1:\mathcal{M}\rightarrow \Gamma_1$ and $\pi_2:\mathcal{M}\rightarrow \Gamma_2$, with $\Gamma_1, \...

Liouville-Arnold's theorem indicates that given a Hamiltonian torus action on a manifold and a set of $n$ functions $F$ from the manifold to $\mathbb{R}^n$ defining an integrable system, the pre image ...