Geodesic
Diffeomorphisms Preserving Symplectic Data on Submanifolds
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Singularities and applications, Tome 267 (2009), pp. 182-197

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We characterize general symplectic manifolds and their structure groups through a family of isotropic or symplectic submanifolds and their diffeomorphic invariance. In this way we obtain a complete geometric characterization of symplectic diffeomorphisms and a reinterpretation of symplectomorphisms as diffeomorphisms acting purely on isotropic or symplectic submanifolds. 
@article{TM_2009_267_a13,
     author = {S. Janeczko and Z. Jelonek},
     title = {Diffeomorphisms {Preserving} {Symplectic} {Data} on {Submanifolds}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {182--197},
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     volume = {267},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2009_267_a13/}
}
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S. Janeczko; Z. Jelonek. Diffeomorphisms Preserving Symplectic Data on Submanifolds. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Singularities and applications, Tome 267 (2009), pp. 182-197. http://geodesic.mathdoc.fr/item/TM_2009_267_a13/