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Resurgence of Receding Limbs

Resurgence of Receding Limbs. Ergodic Methods in Dynamics Bedlewo April 24. 2012. Carsten Lunde Petersen NSM RUC. Joint work Adam Epstein, Warwick University. 1/4. 1/2. 0. 3/4. 1/3 Limb. 2/7. 1/7. Zoom on 1/3 Limb and wake. 1/3 wake and Limb with dyadic sub-wakes. M 1/3 in purple.

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Resurgence of Receding Limbs

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  1. Resurgence of Receding Limbs • Ergodic Methods in Dynamics • Bedlewo April 24. 2012 Carsten Lunde Petersen NSM RUC

  2. Joint work Adam Epstein, Warwick University

  3. 1/4 1/2 0 3/4

  4. 1/3 Limb 2/7 1/7

  5. Zoom on 1/3 Limb and wake

  6. 1/3 wake and Limb with dyadic sub-wakes M1/3 in purple 1/2 3/4 1/4

  7. Sub wakes of 1/3 Limb 3/4 1/4 1/4 1/2 1/2 0 3/4

  8. This explains the notion of Limbs in the Mandelbrot set and its dyadic decorations. • Now we come to the Main topic Quadratic rational maps.

  9. M0,5, σ2-plane

  10. M0 M0.8 M0.9 M1

  11. (-75+33i::5-27i)

  12. (245+108.75i::5-78.75i)

  13. (-7000+3000i::1000-3000i)

  14. M1

  15. The End

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