Nontwist non-Hamiltonian systems

Abstract

We show that the nontwist phenomena previously observed in Hamiltonian systems exist also in time-reversible non-Hamiltonian systems. In particular, we study the two standard collision-reconnection scenarios and we compute the parameter space breakup diagram of the shearless torus. Besides the Hamiltonian routes, the breakup may occur due to the onset of attractors. We study these phenomena in coupled phase oscillators and in non-area-preserving maps.

Area-preserving maps models of gyroaveraged E×B chaotic transport

“…The Slater's Theorem states that, for any quasiperiodic motion on the circle, there are at most three different recurrences, or return times, in any connected interval. Although this theorem was originally formulated for circle maps, it can also be applied to two-dimensional systems, once the dynamics on a KAM curve is mapped to a quasiperiodic rotation on a circle [26]. The recurrence time is defined as the number of iterations that an orbit takes to return to a neighborhood of a point.…”

“…Our criterion is based on the technique proposed in [26], which considers the recurrence properties of the IPO in conjunction with…”

“…[28], the technique described in Ref. [26] was used to study the breakup of the shearless curve in the nontwist standard map. The Slater's Theorem states that, for any quasiperiodic motion on the circle, there are at most three different recurrences, or return times, in any connected interval.…”

“…As shown in Refs. [26,27], the recurrence properties of an orbit provide an efficient and accurate method to differentiate chaotic and non-chaotic motion. A recent example of the application of this technique to the standard nontwist map was presented in Ref.…”

“…To compute the breakup diagrams we follow the technique in Ref. [26] which is based on the application of Slater's theorem [38] to the recurrence properties of orbits. As shown in Refs.…”