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math.DG2016
Metrisability of Painlevé equations
Felipe Contatto, Maciej Dunajski
We solve the metrisability problem for the six Painlevé equations, and more generally for all 2nd order ODEs with Painlevé property, and determine for which of these equations thei…
math.DG2015
First integrals of affine connections and Hamiltonian systems of hydrodynamic type
Felipe Contatto, Maciej Dunajski
We find necessary and sufficient conditions for a local geodesic flow of an affine connection on a surface to admit a linear first integral. The conditions are expressed in terms o…