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Periodically kicked rotor:

Periodically kicked rotor:. Winding Number. Circle map. For the linear map. Ω rational → periodic Ω irrational → quasi-periodic. W=5/8. 2. 7. 5. 0. 4. 1. 3. 6. Continued Fraction. n th order approximation:. Approximation of irrational number by rational fractions.

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Periodically kicked rotor:

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  1. Periodically kicked rotor:

  2. Winding Number Circle map For the linear map Ω rational → periodic Ω irrational → quasi-periodic

  3. W=5/8 2 7 5 0 4 1 3 6

  4. Continued Fraction nth order approximation: Approximation of irrational number by rational fractions

  5. Golden Ratio → Fibonacci series: 1,2,3.5.8….

  6. flowers

  7. Sunflower

  8. Pineapple

  9. Human body

  10. Quasiperiodicity + ? w2 w1

  11. Quasiperiodicity + Torus

  12. Quasiperiodic

  13. Quasiperiodic

  14. Winding Numbers Frequency-ratio parameter: (Rotation number) number of times the trajectory winds around the small cross-section of the torus after going once around the large circumference.

  15. Hopf Bifurcation

  16. Landau route to turbulence

  17. Ruelle-Taken-Newhouse route to Chaos Ref: Argyris etl

  18. Quasiperiodic route to Chaos Ref: Argyris etl

  19. Ref: Argyris etl

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