Delshams A., Ramirez-Ros R.
Poincare-Melnikov-Arnold Method for Analytic Planar Maps
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ABSTRACT. The Poincare-Melnikov-Arnold method for planar maps
gives rise to a Melnikov function defined
by an infinite and (a priori) analytically uncomputable sum.
Under an assumption of meromorphicity, residues theory can be applied
to provide an equivalent finite sum.
Moreover, the Melnikov function turns out to be an elliptic function and
a general criterion about non-integrability is provided.
Several examples are presented with explicit
estimates of the splitting angle.
In particular, the non-integrability of non-trivial symmetric
entire perturbations of elliptic billiards is proved,
as well as the non-integrability of standard-like maps.