1 / 15

Full Families of Multimodal Maps on the Circle

Full Families of Multimodal Maps on the Circle. E. de Faria, W. de Melo, P. Salomão, E. Vargas. GOAL. Find models and parametrize dynamical behaviors. Describe each model or behavior. Multimodal maps on the circle. G(x) mod 1. G(x+1) = G(x) +d. d=2. Multimodal maps on the circle.

banes
Download Presentation

Full Families of Multimodal Maps on the Circle

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Full Families of Multimodal Maps on the Circle E. de Faria, W. de Melo, P. Salomão, E. Vargas

  2. GOAL • Find models and parametrize dynamical behaviors. • Describe each model or behavior.

  3. Multimodal maps on the circle G(x) mod 1 G(x+1) = G(x) +d d=2

  4. Multimodal maps on the circle G a lift of a continuous map g on 3 • 2m – modal • degree d • type 2 G 1 • periodic extrema are attractors; • no wandering intervals; • no intervals of periodic points; • periodic attractors are essential. 0 -1 1 0 m = 4, d = 2 G mod 1

  5. Blaschke Products Control of position of critical values

  6. Theorem:

  7. The family is full Theorem:

  8. History 1 0

  9. Parameter space ii) i)

  10. Realization of finite combinatorics 3) The combinatorics

  11. The map of critical values

More Related