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Rotating accelerator-mode islands.

Oded Barash¹, Itzhack Dana

¹Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|August 7, 2007

Summary

Rotating accelerator-mode islands (RAIs) with quasiregular motion in rotational resonances are confirmed. These RAIs exhibit stickiness, leading to anomalous chaotic transport, differing from forced map accelerator modes.

Area of Science:

Nonlinear dynamics
Chaos theory
Statistical mechanics

Background:

The standard map is a fundamental model in nonlinear dynamics.
Accelerator-mode islands (RAIs) exhibit quasiregular motion in rotational resonances.
Understanding RAI behavior is crucial for analyzing chaotic transport.

Purpose of the Study:

To establish the existence of rotating accelerator-mode islands (RAIs) in the standard map.
To characterize the behavior of RAIs across different orders of resonance and nonintegrability parameters.
To investigate the impact of RAIs on chaotic transport.

Main Methods:

Accurate numerical analysis of existing data.
Investigation of RAIs in rotational resonances (m > 1) of the standard map.

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Examination of RAIs for varying nonintegrability parameter K.

Main Results:

Existence of RAIs performing quasiregular motion is confirmed.
Many RAIs visit resonances of different orders (m <= 3) for small K.
Pure RAIs visiting only m=2 or m=3 resonances exist for large K.
RAIs, regardless of size, cause anomalous chaotic transport due to stickiness.

Conclusions:

RAIs are a confirmed phenomenon in the standard map.
RAI behavior varies with the nonintegrability parameter K.
RAIs significantly influence chaotic transport, distinct from forced map accelerator modes.