Standard twist and non-twist maps

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.

Keywords:
Symplectic Maps; Standard Map; Non-Twist Map; Conservative Systems