Standard twist and non-twist maps

Abstract

Symplectic maps can provide a straightforward and accurate way to visualize and quantify the dynamics of conservative systems with two degrees of freedom. These maps can be easily iterated from the simplest computers to obtain trajectories with great accuracy. Their usage arises in many fields, including celeste mechanics, plasma physics, chemistry, and so on. In this paper we introduce two examples of symplectic maps, the standard map and the standard non-twist map, exploring the phase space transformation as their control parameters are varied. Furthermore, for the non-twist map, we also present, that its chaotic motion is separated in phase space by the non-twist transport barrier.

Basin Entropy and Shearless Barrier Breakup in Open Non-Twist Hamiltonian Systems

“…For relatively small values of k , the system becomes non-integrable and one can observe quasiperiodic orbits spanning the entire interval and invariant curves inside islands centered at a periodic orbit of the map ( 11 ) and ( 12 ). This is a consequence of the non-monotonicity of the winding number profile, i.e., there will be two orbits with the same winding number (a phenomenon also known as degeneracy , and which appears only for non-twist systems) [ 28 ]. For a larger value of the perturbation parameter k , we observe such a collision of periodic orbits, involving a reconnection of the islands’ separatrices.…”