Space of initial conditions for a cubic Hamiltonian system

ABSTRACT

In this paper, we perform the analysis that leads to the space of initial conditions for the Hamiltonian system , , studied by the author in a previous article cited below. By compactifying the phase space of the system from to three base points arise in the standard coordinate charts covering the complex projective space. Each of these is removed by a sequence of three blow-ups, a construction to regularise the system at these points. The resulting space, where the exceptional curves introduced after the first and second blow-up are removed, is the so-called Okamoto’s space of initial conditions for this system which, at every point, defines a regular initial value problem in some coordinate chart of the space. The solutions in these coordinates will be compared to the solutions in the original variables.

KEYWORDS:

• Painleve equations
• space of initial conditions
• Hamiltonian systems

AMS SUBJECT CLASSIFICATIONS:

• 34M55
• 34M35

Notes

No potential conflict of interest was reported by the author.