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.

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 and the standard non-twist map, exploring the phase space transformation as their control parameters are varied.

Some internal transport barriers in tokamaks have been related to the vicinity of extrema of the plasma equilibrium profiles. This effect is numerically investigated by considering the guiding-centre trajectories of plasma particles undergoing $\boldsymbol {E}\times \boldsymbol {B}$ drift motion, considering that the electric field has a stationary non-monotonic radial profile and an electrostatic fluctuation. In addition, the equilibrium configuration has a non-monotonic safety factor profile. The numerical integration of the equations of motion yields a symplectic map with shearless barriers. By changing the safety factor profile parameters, the appearance and breakup of these shearless curves are observed. The shearless curve's successive breakup and recovery are explained using concepts from bifurcation theory. We also present bifurcation sequences associated with the creation of multiple shearless curves. Physical consequences of scenarios with multiple shearless curves are discussed.

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