Dynamics and statistics of weak chaos in a 4-D symplectic map (Q6608631)

In this paper, the authors explore the so-called weak chaos in a four-dimensional symplectic map, an extension of the two-dimensional MacMillan map. Their study focuses on the phenomenon of ``stickiness'' whereby chaotic orbits linger near regions of regular motion. Using coupled MacMillan maps, the authors analyse chaotic dynamics near unstable fixed points, and investigate statistical properties using the central limit theorem. They show that weak chaos is characterised by long-range correlations and probability distributions that differ from the Gaussian distributions typical of strong chaos. The paper explains how the intensity of chaos and its statistical features depend on system parameters. As the system becomes more nonlinear, chaotic behavior intensifies, and the statistical profiles deviate further from Gaussian behavior. The authors' findings suggest that weak chaos is a common feature of multi-dimensional conservative systems, with implications for fields like celestial mechanics and particle accelerator dynamics.\N\NFor the entire collection see [Zbl 1533.37005].