symplectic leaf
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Author(s):  
Nicolai Reshetikhin ◽  
Gus Schrader

Abstract In this paper we prove superintegrability of Hamiltonian systems generated by functions on $K\backslash G/K$, restricted to a symplectic leaf of the Poisson variety $G/K$, where $G$ is a simple Lie group with the standard Poisson Lie structure, and $K$ is its subgroup of fixed points with respect to the Cartan involution.



2008 ◽  
Vol 144 (3) ◽  
pp. 774-786 ◽  
Author(s):  
Jean-Paul Dufour ◽  
Aïssa Wade

AbstractWe give a local normal form for Dirac structures. As a consequence, we show that the dimensions of the pre-symplectic leaves of a Dirac manifold have the same parity. We also show that, given a point m of a Dirac manifold M, there is a well-defined transverse Poisson structure to the pre-symplectic leaf P through m. Finally, we describe the neighborhood of a pre-symplectic leaf in terms of geometric data. This description agrees with that given by Vorobjev for the Poisson case.



2001 ◽  
Vol 54 ◽  
pp. 249-274 ◽  
Author(s):  
Yurii Vorobjev


1991 ◽  
Vol 156 (1-2) ◽  
pp. 96-100 ◽  
Author(s):  
Huanchun Ye ◽  
P.J. Morrison


1988 ◽  
Vol 134 (1) ◽  
pp. 19-24 ◽  
Author(s):  
John David Crawford ◽  
Peter D. Hislop


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