Non-autonomous standard nontwist map

Abstract

Area-preserving nontwist maps locally violate the twist condition, giving rise to shearless curves. Nontwist systems appear in different physical contexts, such as plasma physics, climate physics, classical mechanics, etc. Generic properties of nontwist maps are captured by the standard nontwist map, which depends on a convection parameter $a$ and a modulation coefficient $b$. In the spirit of non-autonomous systems, we consider the standard nontwist map (SNM) with a linearly increasing modulation coefficient, and we investigate the evolution of an ensemble of points on the phase space that initially lies on the shearless invariant curve in the initial state, called shearless snapshot torus. Differently from the SNM with constant parameters -- where we can see different scenarios of collision/annihilation of periodic orbits leading to global transport, depending on the region in the parameter space -- for the SNM with time-dependent parameters, the route to chaos is not only related to the path in the $(a, b)$ parameter space, but also to the scenario of the evolution of parameter $b_n$. In this work, we identify power-law relationships between key parameters for the chaotic transition and the iteration time. Additionally, we analyze system reversibility during the chaotic transition and demonstrate an extra transport, where parameter variation modifies the diffusion coefficient.