Long-Time Correlations and Anomalous Diffusion Due to Accelerator Modes in the Standard Maps

From Dispersion to Laminarity in Dynamical Systems

“…A useful example which shows a similar behavior is provided by the standard map [1,2,10,11]. Here the motion is dictated by the iteration scheme…”

“…The fundamental accelerating modes p = I are found to be particularly efficient in the enhancement of the diffusion. Enhanced diffusion due to temporal resonances with the p = 1 = 3 {K ~ 1.1) and with the p = I = 5 fundamental modes have been observed [10,11].…”

“…The stability islands arise around fixed points which can be classified according to two arguments p and /: p denotes the period, so that 9n + p = 9n, and / denotes the displacement, so that |x"+p -x j = /. Hierarchies of stability islands can show up in the vicinity of basic p -I fixed points [10]. The fundamental accelerating modes p = I are found to be particularly efficient in the enhancement of the diffusion.…”

“…One finds diffusion anomalies in numerical studies of one-dimensional maps [4,5,9], of the Chirikov-Taylor standard map [1,2,10,11], of stochastic webs [7], and of conservative motion in two-dimensional potential surfaces [6,12]. Experimentally, anomalies have been observed for tracer diffusion in flow systems [13][14][15].…”

“…In particular it has been observed that particles' orbits do not necessarily obey simple Gaussian behavior, rather they may exhibit an intermittent laminar chaotic behavior which results in dispersive or enhanced diffusional motion [3][4][5][6][7][8][9][10].…”