Summability of first integrals of a $C^\omega$-non-integrable resonant Hamiltonian system
Volume 97 / 2012
Banach Center Publications 97 (2012), 169-178
MSC: Primary 34M30; Secondary 37F50, 37G05.
DOI: 10.4064/bc97-0-13
Abstract
This article studies the summability of first integrals of a $C^\omega$-non-integrable resonant Hamiltonian system. The first integrals are expressed in terms of formal exponential transseries and their Borel sums. Smooth Liouville integrability and a relation to the Birkhoff transformation are discussed from the point of view of the summability.
