Title: Stokes phenomenon and confluence in non-autonomous Hamiltonian systems,
Abstract: This article studies a confluence of a pair of regular singular points to an
irregular one in a generic family of time-dependent Hamiltonian systems in
dimension 2. This is a general setting for the understanding of the
degeneration of the sixth Painleve equation to the fifth one. The main result
is a theorem of sectoral normalization of the family to an integrable formal
normal form, through which is explained the relation between the local
monodromy operators at the two regular singularities and the non-linear Stokes
phenomenon at the irregular singularity of the limit system. The problem of
analytic classification is also addressed.
Key words: Non-autonomous Hamiltonian systems; irregular singularity;
non-linear Stokes phenomenon; wild monodromy; confluence; local analytic
classification; Painleve equations.