Geodesic
Hamiltonian dynamical systems with even and odd Poisson brackets
Teoretičeskaâ i matematičeskaâ fizika, Tome 79 (1989) no. 1, pp. 117-126 
D. V. Volkov; A. I. Pashnev; V. A. Soroka; V. I. Tkach. Hamiltonian dynamical systems with even and odd Poisson brackets. Teoretičeskaâ i matematičeskaâ fizika, Tome 79 (1989) no. 1, pp. 117-126. http://geodesic.mathdoc.fr/item/TMF_1989_79_1_a10/
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     title = {Hamiltonian dynamical systems with even and odd {Poisson} brackets},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {117--126},
     year = {1989},
     volume = {79},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1989_79_1_a10/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Using the example of the supersymmetric Witten mechanics we prove that the Hamiltonian systems with equal number of Grassmann even and Grassmann odd canonical variables are inherently characterized by the odd Poisson bracket in addition to the even one. The duality between even and odd integrals of motion under the change of the Poisson brackets parity is established for such systems.

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