The Role of a Steepness Parameter in the Exponential Stability of a Model Problem. Numerical Aspects

The Nekhoroshev theorem considers quasi integrable Hamiltonians providingstability 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 implynumerically observable differences in the stability times.After a recent study on this problem (Guzzo et al. 2011, Todorovic et al. 2011) we show some additional numerical resultson 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 parametersmoothly regulates the steepness properties in the model.