Geodesic
Hamiltonians associated with the third and fifth Painlevé equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 162 (2010) no. 1, pp. 69-74 Cet article a éte moissonné depuis la source Math-Net.Ru

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We obtain a Painlevé-type differential equation for the simplest rational Hamiltonian associated with the fifth Painlevé equation in the case $\gamma\ne0$, $\delta=0$. We prove the existence of Hamiltonians of a nonrational type associated with the fifth Painlevé equation in the case $\gamma\ne0$, $\delta=0$. We obtain a generalization of the Garnier and Okamoto formulas for rational Hamiltonians associated with the third Painlevé equation.
Mots-clés : third Painlevé equation, fifth Painlevé equation
Keywords: Hamiltonian. 
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V. V. Tsegel'nik. Hamiltonians associated with the third and fifth Painlevé equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 162 (2010) no. 1, pp. 69-74. http://geodesic.mathdoc.fr/item/TMF_2010_162_1_a2/

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