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- Non-squeezing_theorem abstract "The non-squeezing theorem, also called Gromov's non-squeezing theorem, is one of the most important theorems in symplectic geometry. It was first proven in 1985 by Mikhail Gromov.The theorem states that one cannot embed a sphere into a cylinder via a symplectic map unless the radius of the sphere is less than or equal to the radius of the cylinder. The importance of this theorem is as follows: very little was known about the geometry behind symplectic transformations. One easy consequence of a transformation being symplectic is that it preserves volume. One can easily embed a ball of any radius into a cylinder of any other radius by a volume-preserving transformation: just picture squeezing the ball into the cylinder (hence, the name non-squeezing theorem). Thus, the non-squeezing theorem tells us that, although symplectic transformations are volume-preserving, it is much more restrictive for a transformation to be symplectic than it is to be volume-preserving.".
- Non-squeezing_theorem wikiPageExternalLink 1208.5969v1.
- Non-squeezing_theorem wikiPageExternalLink ewmcambrevjn23.pdf.
- Non-squeezing_theorem wikiPageID "23825035".
- Non-squeezing_theorem wikiPageLength "5912".
- Non-squeezing_theorem wikiPageOutDegree "17".
- Non-squeezing_theorem wikiPageRevisionID "652126998".
- Non-squeezing_theorem wikiPageWikiLink Canonical_coordinates.
- Non-squeezing_theorem wikiPageWikiLink Canonical_transformation.
- Non-squeezing_theorem wikiPageWikiLink Category:Symplectic_geometry.
- Non-squeezing_theorem wikiPageWikiLink Category:Theorems_in_geometry.
- Non-squeezing_theorem wikiPageWikiLink Dusa_McDuff.
- Non-squeezing_theorem wikiPageWikiLink Eye_of_the_Needle.
- Non-squeezing_theorem wikiPageWikiLink Eye_of_the_needle.
- Non-squeezing_theorem wikiPageWikiLink Ian_Stewart_(mathematician).
- Non-squeezing_theorem wikiPageWikiLink Liouvilles_theorem_(Hamiltonian).
- Non-squeezing_theorem wikiPageWikiLink Maurice_A._de_Gosson.
- Non-squeezing_theorem wikiPageWikiLink Mikhail_Leonidovich_Gromov.
- Non-squeezing_theorem wikiPageWikiLink Phase_space.
- Non-squeezing_theorem wikiPageWikiLink Symplectic_form.
- Non-squeezing_theorem wikiPageWikiLink Symplectic_geometry.
- Non-squeezing_theorem wikiPageWikiLink Symplectic_vector_space.
- Non-squeezing_theorem wikiPageWikiLink Symplectomorphism.
- Non-squeezing_theorem wikiPageWikiLink Symplectomorphisms.
- Non-squeezing_theorem wikiPageWikiLink Uncertainty_principle.
- Non-squeezing_theorem wikiPageWikiLinkText "Gromov's non-squeezing theorem".
- Non-squeezing_theorem wikiPageWikiLinkText "Non-squeezing theorem".
- Non-squeezing_theorem wikiPageWikiLinkText "non-squeezing theorem".
- Non-squeezing_theorem hasPhotoCollection Non-squeezing_theorem.
- Non-squeezing_theorem wikiPageUsesTemplate Template:%22.
- Non-squeezing_theorem wikiPageUsesTemplate Template:Reflist.
- Non-squeezing_theorem subject Category:Symplectic_geometry.
- Non-squeezing_theorem subject Category:Theorems_in_geometry.
- Non-squeezing_theorem type Theorem.
- Non-squeezing_theorem comment "The non-squeezing theorem, also called Gromov's non-squeezing theorem, is one of the most important theorems in symplectic geometry. It was first proven in 1985 by Mikhail Gromov.The theorem states that one cannot embed a sphere into a cylinder via a symplectic map unless the radius of the sphere is less than or equal to the radius of the cylinder. The importance of this theorem is as follows: very little was known about the geometry behind symplectic transformations.".
- Non-squeezing_theorem label "Non-squeezing theorem".
- Non-squeezing_theorem sameAs Théorème_de_non-plongement_de_Gromov.
- Non-squeezing_theorem sameAs 심플렉틱_용량.
- Non-squeezing_theorem sameAs m.06_w6_v.
- Non-squeezing_theorem sameAs Q3527214.
- Non-squeezing_theorem sameAs Q3527214.
- Non-squeezing_theorem wasDerivedFrom Non-squeezing_theorem?oldid=652126998.
- Non-squeezing_theorem isPrimaryTopicOf Non-squeezing_theorem.