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Results tagged with sg.symplectic-geometry
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user 766
Hamiltonian systems, symplectic flows, classical integrable systems
43
votes
1
answer
3k
views
Is a symplectic camel actually prohibited from passing through the eye of a needle?
Gromov's symplectic nonsqueezing theorem asserts that in the symplectic space ${\bf R}^{2n}$ with canonical coordinates $p_1,\dots,p_n,q_1,\dots,q_n$, and two radii $0 < r < R$, it is not possible to …
- 114k
101
votes
5
answers
11k
views
Is there a high level reason why the inverse square law of gravitation yields periodic orbit...
Given a spherically symmetric potential $V: {\bf R}^d \to {\bf R}$, smooth away from the origin, one can consider the Newtonian equations of motion
$$ \frac{d^2}{dt^2} x = - (\nabla V)(x)$$
for a part …
- 114k