127 citations · 780 across the 73 of their papers we have counts for
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Integration of a generalized Hénon-Heiles Hamiltonian
C. Verhoeven, M. Musette, R. Conte
The generalized Hénon-Heiles Hamiltonian with an additional nonpolynomial term is known to be Liouville integrable for thr…
New contiguity relation of the sixth Painlevé equation from a truncation
Robert Conte, Micheline Musette
For the master Painlevé equation P6(u), we define a consistent method, adapted from the Weiss truncation for partial differential equations, which allows us to obtain the first deg…
A truncation for obtaining all the first degree birational transformations of the Painlevé transcendents
Robert Conte, Micheline Musette
A birational transformation is one which leaves invariant an ordinary differential equation, only changing its parameters. We first recall the consistent truncation which has allow…
First degree birational transformations of the Painlevé equations and their contiguity relations
Robert Conte, Micheline Musette
We present a consistent truncation, allowing us to obtain the first degree birational transformation found by Okamoto for the sixth Painlevé equation. The discrete equation arising…
On the Schlesinger transformations of the sixth Painlevé equation
Robert Conte
Following the recent discovery of two new Schlesinger transformations (ST) for the sixth Painlevé equation, we give the interrelations between all the known STs. We thus isolate th…