Nonsqueezing theorem - a proof with the action

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SUMMARY

The discussion centers on Gromov's nonsqueezing theorem, which asserts that a sphere cannot be symplectically transformed into a cylinder. The proof utilizes the concept of action as a symplectic invariant, expressed in terms of the radii of both the sphere and the cylinder. The original poster sought a detailed reference for this proof and ultimately found it in Gosson's book on page 100. This highlights the importance of understanding symplectic invariants in the context of nonsqueezing theorems.

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  • Understanding of symplectic geometry
  • Familiarity with Gromov's nonsqueezing theorem
  • Knowledge of symplectic invariants
  • Basic concepts of Hamiltonian mechanics
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  • Study Gromov's nonsqueezing theorem in detail
  • Explore symplectic invariants and their applications
  • Read Gosson's book for insights on the action in symplectic geometry
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Mathematicians, physicists, and students of symplectic geometry seeking to deepen their understanding of nonsqueezing theorems and symplectic invariants.

mma
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I've read somewhere a proof of Gromov's nonsqueezing theorem using the fact that the action is a symplectic invariant (just like the Hamiltonian). As far as I remember, the action was expressed in terms of the radius of a sphere and also in terms of the radius of a cylinder, and the proof of the statement that the sphere doesn't fit by symplectic transormation into the cylinder was based on these expressions. But I 've read this poof only very superficially and just now wanted to read it in details, but now I don't find it, and don't remember where it was. Does somebody know this proof? Coul'd somebody tell me where can I find it?
Thanks in advance.
 
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Don't trouble, I found it in Gosson's book on page 100. (perhaps this isn't that I saw originally, but it doesn't matter)
 

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