The role of a steepness parameter in the exponential stability of a model problem: Numerical aspects

Abstract

The Nekhoroshev theorem considers quasi integrable Hamiltonians providing stability of actions in exponentially long times. One of the hypothesis required by the theorem is a mathematical condition called steepness. Nekhoroshev conjectured that different steepness properties should imply numerically observable differences in the stability times. After a recent study on this problem (Guzzo et al. 2011, Todorović et al. 2011) we show some additional numerical results on the change of resonances and the diffusion laws produced by the increasing effect of steepness. The experiments are performed on a 4-dimensional steep symplectic map designed in a way that a parameter smoothly regulates the steepness properties in the model.

Keywords

• Celestial mechanics
• Methods: numerical