Viscosity Solutions Methods for Converse Kam Theory
نویسندگان
چکیده
The main objective of this paper is to prove new necessary conditions to the existence of KAM tori. These converse KAM conditions, can be used to detect gaps between KAM tori and Aubry-Mather sets. By exploring the connections between viscosity solutions of Hamilton-Jacobi equations, KAM and Aubry-Mather theories we develop a set of explicit a-priori estimates for smooth viscosity solutions that are valid in any space dimension, and can be checked numerically. We apply our results to detect non-integrable regions in several examples: a forced pendulum, two coupled penduli, and the double pendulum.
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