Pieces of two possible orbits in the proposed model. The upper trajectory illustrates a situation where the particle enters into and leaves from the electric field region at x = 0. The lower trajectory illustrates a situation where the particle enters into the electric field at the left side and leaves this region at x = d.
These plots display the phase space of the system for different control parameters: (a) and , (b) and , (c) and and (d) and .
These plots illustrate the average Lyapunov exponent as function of: (a) for constant and; (b) as function of for fixed .
This figure shows the position of the lowest energy invariant KAM curves for different values of and considering: (a) ; (b) ; and (c) .
The figure shows the average of the absolute values of the velocity of the KAM curves as function of for three different values of . The best fits furnish with .
(a) shows the plot of the normalized number of escaping orbits at the iteration n for different values of and fixed . (b) displays the overlap of all curves shown in (a) onto a single plot, after a suitable rescaling of the axis.
(a) illustrates the crossover as function of . The best fit furnishes with z = −0.98 ± 0.02. (b) illustrates the maximum values of h as function of . The best fit furnishes with .
(a) displays the normalized number of remaining orbits (do not escape) as function of n and different values of ; (b) illustrates the decay of the quantity showing evidently two regimes.
(a) shows the numerical data of crossover of . The best fit furnishes with . Appropriate scaling transformation overlaps the curves onto a single plot, as displayed in (b).
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