Solution with movable singular points of some Hamiltonian system

Abstract

This paper studies the movable singular points of a solution of the Hamiltonian system with the Hamiltonian H ≔ H 0 + H 1 H≔H_0+H_1 . Here H 0 H_0 is integrable and the Hamiltonian system of H 0 H_0 has a singular solution v v , while H 1 H_1 is a perturbation. A singular solution for H H is given as F ( v ) F(v) for some transformation F F being defined in the domain of the phase space which contains the orbit of v v tending to the infinity. The map F F is given by the homology equation via the global Borel summability.