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Hamiltonian systems, symplectic flows, classical integrable systems

28 votes
Accepted

Is $\Bbb S^2 \times \Bbb S^4$ symplectic?

No. Note that $H^2(S^2\times S^4,\mathbb R)$ is one dimensional, spanned by $\pi^*\alpha$, where $\pi:S^2\times S^4\to S^2$ is the projection, and $\alpha$ is a volume form on $S^2$. Suppose $\omega$ …
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Momentum a cotangent vector

$p$ is the differential of L with respect to the second variable ($\dot q$), so it represents a linear functional on the tangent space at $q, \dot q$), given by $$ (u,v)\to \frac{d}{dt} L(q,\dot q+tv …
Fan Zheng's user avatar
  • 5,169