Transporte e simetria em sistemas Hamiltonianos não twist

Abstract

The standard nontwist map is a simple and general example of Hamiltonian systems that does not satisfy the twist condition. The map applications cover phenomenons related to plasmas, celestial mechanics, wave guides, particle accelerators and other examples. The presence of twin islands chains and the shearless curve has a big influence over barriers in the phase space and, consequently, over the transport through the space. In this work, we provide a connection between turnstiles, the manifolds intersection scenario and the transport in the phase space. This connection is still not completely understood in non twist Hamiltonian systems. The high transport is associated to the intercrossing scenario and how the homoclinic and heteroclinic points from different islands chains are close to each other and how the turnstiles act like a transport mechanism. The turnstile is the gate or the barrier to the trajectories from one region of the phase space to another. The low transport is represented by the opposite scenario, the intracrossing scenario has a larger distance between the intersection points. In this case, the turnstiles act as a trapping mechanism. The standard nontwist map is a symmetric map, i.e, there is not a preferential direction for the trajectories to follow. However, the addition of a new perturbation with a shape as csin(2πmx) is able to break the symmetry, if m is even, and the directed transport is a possible phenomenon to exist in the phase space. The map with the new perturbation is called extended standard nontwist map and it features interested phenomenon as the symmetry breaking, directed transport and the recovery of the monotonic scenario, which is not present in the original nontwist map.