We investigate the prevalence of multistability in the parameter space of the kicked rotor map. We report high-resolution phase diagrams showing how the density of attractors and the density of periods vary as a function of both model parameters. Our diagrams illustrate density variations that exist when moving between the familiar conservative and strongly dissipative limits of the map. We find the kicked rotor to contain multistability regions with more than 400 coexisting attractors. This fact makes the rotor a promising high-complexity local unit to investigate synchronization in networks of chaotic maps, in both regular and complex topologies.

This paper investigates the stability of off-axis continuous intense relativistic beams propagating inside a circular conducting pipe. The equations of motion for the centroid and the envelope of slightly off-axis beams are derived and used to determine equilibrium and stability conditions for the beam transport. It is shown that depending on the parameters of the system, beams propagating along the pipe axis may become unstable due to the presence of the wall, imposing a fundamental limitation in the effective area that an equilibrium beam can occupy inside the conductor.

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