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Lyapunov and diffusion timescales in the Solar system 3. Chaos “due to encounters”

Lyapunov and diffusion timescales in the Solar system 3. Chaos “due to encounters”. I. I. Shevchenko Pulkovo Observatory. Abstract.

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Lyapunov and diffusion timescales in the Solar system 3. Chaos “due to encounters”

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  1. Lyapunov and diffusion timescales in the Solar system3. Chaos “due to encounters” I. I. Shevchenko Pulkovo Observatory

  2. Abstract We consider chaos “due to encounters” in the dynamics of the Solar system bodies. This terminology is conventional, because the essential source of chaos is the same: interaction of resonances.

  3. The encounter map Murray C.D., Dermott S.F. Solar SystemDynamics(1999).

  4. The encounter map

  5. The encounter map

  6. The μ2/7 law

  7. The μ2/7 law

  8. The μ2/7 law Murray C.D., Dermott S.F. Solar SystemDynamics(1999).

  9. The Kepler map The Kepler map was derived by Petrosky (1986) and Chirikov and Vecheslavov (1986) in the framework of the restricted three-body and four-body problems in order to describe the long-term chaotic orbital behaviour of Halley’s comet and, generally, that of the comets in nearly parabolic motion. It is a two-dimensional area-preserving map, describing a comet’s motion in terms of energy and time. Its second equation is based on Kepler’s third law, hence the name of the map. Since 1980s the Kepler map has become paradigmatic in a number of applications in celestial mechanics and in atomic physics. It represents an important kind of general separatrix maps.

  10. The Kepler map

  11. The Kepler map • Petrosky, T.Y., Phys. Letters A117, 328 (1986). • Chirikov, B.V. and Vecheslavov, V.V., INP Preprint 86–184 (1986). • Petrosky, T.Y. and Broucke, R., Celest. Mech. 42, 53 (1988).

  12. 1986

  13. Kepler’s third law

  14. The parabolic motion

  15. Elementary derivation of the Kepler map

  16. Elementary derivation of the Kepler map

  17. Elementary derivation of the Kepler map

  18. Elementary derivation of the Kepler map

  19. Elementary derivation of the Kepler map

  20. Elementary derivation of the Kepler map

  21. Elementary derivation of the Kepler map

  22. Elementary derivation of the Kepler map

  23. The chaotic layer

  24. The μ2/5 law

  25. Applications in astronomy

  26. Applications in physics

  27. Comets and NEAs

  28. Comets and NEAs

  29. Comets and NEAs

  30. The Lyapunov times of comets

  31. The Lyapunov exponents of Kepler maps

  32. The Lyapunov times of comets

  33. Comets and prehistory of the Kepler map

  34. The Kepler map

  35. The Kepler map among other maps

  36. General separatrix maps

  37. Hamiltonian intermittency

  38. Hamiltonian intermittency

  39. Hamiltonian intermittency

  40. Hamiltonian intermittency

  41. Hamiltonian intermittency

  42. Hamiltonian intermittency

  43. Hamiltonian intermittency

  44. Hamiltonian intermittency

  45. Hamiltonian intermittency

  46. Hamiltonian intermittency

  47. Hamiltonian intermittency

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