  Crossing the transition energy is always a delicate process, representing a
potential source of strong perturbations of the dynamics of charged particle
beams in a hadron circular accelerator. Since the first generation of multi-GeV
rings, intense studies have been devoted to understanding the possible harmful
mechanisms involved in transition crossing and to devise mitigation measures.
Nowadays, several circular particle accelerators are successfully operating
across transition and this process is well mastered. In a completely different
context, stable resonances of the traverse phase space have been proposed as
new means of manipulating charged particle beams. While the original aim of
such a proposal was multi-turn extraction from the CERN Proton Synchrotron to
the Super Proton Synchrotron, many more applications have been proposed and
studied in detail. In this paper, the two topics, i.e. transition crossing and
stable resonances, have been brought together with the goal of providing a
novel and non-adiabatic approach to perform a clean transition crossing. The
idea presented here is that by judiciously using sextupoles and octupoles it is
possible to generate stable islands of the horizontal phase space. These
islands represent a second closed orbit whose properties can be selected
independently of those of the standard, i.e. central, closed orbit. This
provides a means of performing a non-adiabatic change of the transition energy
experienced by the charged particles by displacing the beam between the two
closed orbits.
