Geodesic
Hamiltonian dynamical systems with even and odd Poisson brackets
Teoretičeskaâ i matematičeskaâ fizika, Tome 79 (1989) no. 1, pp. 117-126

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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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     author = {D. V. Volkov and A. I. Pashnev and V. A. Soroka and V. I. Tkach},
     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},
     publisher = {mathdoc},
     volume = {79},
     number = {1},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1989_79_1_a10/}
}
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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/