Transport of chaotic trajectories from regions distant from or near to structures of regular motion of the Fermi-Ulam model

Abstract

The chaotic portion of phase space of the simplified Fermi-Ulam model is studied under the context of transport of trajectories in two scenarios: (i) the trajectories are originated from a region distant from the islands of regular motion and are transported to a region located at a high portion of phase space and (ii) the trajectories are originated from chaotic regions around the islands of regular motion and are transported to other regions around islands of regular motion. The transport is investigated in terms of the observables histogram of transport and survival probability. We show that the histogram curves are scaling invariant and we organize the survival probability curves in four kinds of behavior, namely (a) transition from exponential decay to power law decay, (b) transition from exponential decay to stretched exponential decay, (c) transition from an initial fast exponential decay to a slower exponential decay, and (d) a single exponential decay. We show that, depending on choice of the regions of origin and destination, the transport process is weakly affected by the stickiness of trajectories around islands of regular motion.

Estudo do comportamento da entropia em bilhares

“…Depending on the region in the phase space the diffusion may be normal or anomalous. From a physical point of view, diffusion in phase space is present in many problems, such as the unlimited growth of energy, 1 [12,13,14], or the study of transport properties from one region of phase space to another region [15,16], and plasma dynamics [17,18], among others.…”