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Understanding the Chaotic Layer Width in Hamiltonian Dynamics: Insights from Nonlinear Resonance

This work delves into the chaotic layer theory in Hamiltonian dynamics, specifically analytical methods for estimating the chaotic layer width of nonlinear resonance. The paper discusses the 3/1 resonance and its chaotic domain estimates (eJ = 0.030, 0.048, 0.060) based on research from Meiss (2008). Topics include the standard map, the separatrix, fast and slow chaos, and marginal resonances, with applications to the rotational dynamics of celestial bodies such as Hyperion, Miranda-Umbriel, Mimas-Tethys, and Prometheus-Pandora systems.

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Understanding the Chaotic Layer Width in Hamiltonian Dynamics: Insights from Nonlinear Resonance

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  1. Width of the chaotic layer I. I. Shevchenko Pulkovo Observatory

  2. Abstract Some elements of the chaotic layer theory in Hamiltonian dynamics are considered and discussed. Namely, these elements comprise the methods of analytical estimation of width of the chaotic layer of nonlinear resonance.

  3. The 3/1 resonance:extent of chaotic domains eJ = 0.030 eJ = 0.048 eJ = 0.060

  4. The standard map at K = KG MeissJ.D., Pramana – Journal of Physics 70, 965 (2008).

  5. The standard map at K = KG and K = 2 MeissJ.D., Pramana – Journal of Physics 70, 965 (2008).

  6. Separatrix split

  7. The standard map

  8. Early estimates

  9. The pendulum f

  10. Interaction of resonances

  11. The separatrix map

  12. The separatrix map In the case of “fast” chaos: yb=̃λ (Chirikov, 1979).

  13. The chaotic layer. Fast chaos

  14. The chaotic layer. Slow chaos

  15. Width of the chaotic layer

  16. Adiabatic chaos

  17. Width of the chaotic layer

  18. Width of the chaotic layer

  19. Marginal resonances

  20. Marginal resonances

  21. Marginal resonances

  22. Marginal resonances

  23. Chaos in rotation of Hyperion and other satellites

  24. Rotational dynamics of minor satellites

  25. Rotation of satellites: the separatrix map

  26. Rotation of Hyperion: width of the chaotic layer

  27. The Miranda–Umbriel system

  28. The Mimas–Tethys system

  29. The Prometheus–Pandora system

  30. The Prometheus–Pandora system

  31. The Prometheus–Pandora system: width of the chaotic layer

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