Near strongly resonant periodic orbits in a Hamiltonian system.
We study an analytic Hamiltonian system near a strongly resonant periodic orbit. We introduce a modulus of local analytic classification. We provide asymptotic formulae for the exponentially small splitting of separatrices for bifurcating hyperbolic periodic orbits. These formulae confirm a conjecture formulated by V. I. Arnold in the early 1970s.
Gelfreich
Vassili
V
Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom. gelf@maths.warwick.ac.uk