Symplectic nonsqueezing: Difference between revisions
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'''Symplectic nonsqueezing''' is the phenomenon that a Hamiltonian flow (or slightly more generally, a symplectomorphism) cannot deform a ball of radius ''R'' into a subset of a cylinder of radius ''r'' whenever ''r < R''. This phenomenon was demonstrated rigorously by Gromov in the finite dimensional case, but generalizing this result to infinite dimensions can require remarkably subtle analysis. | '''Symplectic nonsqueezing''' is the phenomenon that a Hamiltonian flow (or slightly more generally, a symplectomorphism) cannot deform a ball of radius ''R'' into a subset of a cylinder of radius ''r'' whenever ''r < R''. This phenomenon was demonstrated rigorously by [http://en.wikipedia.org/wiki/Mikhail_Gromov M. Gromov] in the finite dimensional case, but generalizing this result to infinite dimensions can require remarkably subtle analysis. Gromov's proof relied upon [http://en.wikipedia.org/wiki/Pseudoholomorphic_curve pseudoholomorphic curves]. | ||
[[Category:Concept]] | [[Category:Concept]] | ||
Latest revision as of 14:10, 27 March 2007
Symplectic nonsqueezing is the phenomenon that a Hamiltonian flow (or slightly more generally, a symplectomorphism) cannot deform a ball of radius R into a subset of a cylinder of radius r whenever r < R. This phenomenon was demonstrated rigorously by M. Gromov in the finite dimensional case, but generalizing this result to infinite dimensions can require remarkably subtle analysis. Gromov's proof relied upon pseudoholomorphic curves.
