Fermi Acceleration in anti-integrable limits of the standard map

TL;DR

This paper investigates a dynamical system modeling high-energy behavior in mechanical models, establishing conditions that ensure the set of orbits exhibiting Fermi acceleration is of measure zero, thus limiting unbounded energy growth.

Contribution

It provides new conditions under which Fermi acceleration orbits are measure zero in a semi-infinite cylindrical dynamical system.

Findings

Fermi acceleration orbits are measure zero under certain conditions

Conditions for high-energy orbit behavior are established

The model relates to anti-integrable limits of the standard map

Abstract

We consider a dynamical system on the semi-infinite cylinder which models the high energy dynamics of a family of mechanical models. We provide conditions under which we ensure that the set of orbits undergoing Fermi acceleration has measure zero.