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Lyapunov and diffusion timescales in the Solar system 1. Separatrix maps and chaotic layers

Lyapunov and diffusion timescales in the Solar system 1. Separatrix maps and chaotic layers. I. I. Shevchenko Pulkovo Observatory. Abstract.

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Lyapunov and diffusion timescales in the Solar system 1. Separatrix maps and chaotic layers

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  1. Lyapunov and diffusion timescales in the Solar system1. Separatrix maps and chaotic layers I. I. Shevchenko Pulkovo Observatory

  2. Abstract Some elements of the chaotic layer theory in Hamiltonian dynamics are considered and discussed. In particular, these elements comprise the methods of analytical estimation of the maximum Lyapunov exponent of the motion within the layer.

  3. The pendulum f

  4. The Kapitsa pendulum

  5. Divided phase space

  6. Interaction of resonances

  7. The separatrix map

  8. The separatrix map

  9. The chaotic layer. Fast chaos

  10. The chaotic layer. Slow chaos

  11. Chaos ingredients

  12. Lyapunov exponents

  13. Lyapunov exponents: computation

  14. Lyapunov exponents

  15. LCE spectra

  16. Analytical estimation of Lyapunov exponents

  17. Analytical estimation of Lyapunov exponents

  18. The separatrix map

  19. Maximum Lyapunov exponent of the separatrix map

  20. Adiabatic chaos

  21. Adiabatic chaos and Lyapunov exponents

  22. Adiabatic chaos and Lyapunov exponents

  23. Adiabatic chaos and Lyapunov exponents

  24. Adiabatic chaos and Lyapunov exponents

  25. Resonance multiplets and Lyapunov exponents

  26. Resonance multiplets and Lyapunov exponents

  27. Resonance multiplets and Lyapunov exponents

  28. The standard map: a multiplet model

  29. The standard map: a phase portrait

  30. The standard map: L(K)

  31. The standard map: L(K)

  32. The standard map: L(K)

  33. Multiplets and the standard map

  34. The standard map at high values of K

  35. The standard map: diffusion

  36. The standard map: diffusion

  37. Diffusion across a chaotic layer

  38. Diffusion in resonance doublets

  39. Diffusion in resonance doublets

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