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Multimodal Maps and Families of Dynamical Behaviors: A Study of Critical Values

This paper explores the intricate world of multimodal maps, focusing on the Circle model. The authors analyze various families of dynamical behaviors, striving to find models and parametrize them effectively. The study highlights the construction of critical value maps, with an emphasis on finite combinatorics and the unique features of the Thurston map. By detailing each model and its distinct behaviors, this work contributes to our understanding of dynamical systems within the context of critical values and their histories.

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Multimodal Maps and Families of Dynamical Behaviors: A Study of Critical Values

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  1. Full Families on 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 3 2 G 1 0 -1 1 0

  4. Blaschke Products

  5. History 1 0

  6. ii) i)

  7. The map of critical values

  8. Realization of finite combinatorics

  9. Thurston map

  10. Uniqueness

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