Displaying similar documents to “Non-uniformly expanding dynamics in maps with singularities and criticalities”

On unimodal maps with critical order 2 + ε

Simin Li, Weixiao Shen (2006)

Fundamenta Mathematicae

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It is proved that a smooth unimodal interval map with critical order 2 + ε has no wild attractor if ε >0 is small.

Statistical properties of unimodal maps

Artur Avila, Carlos Gustavo Moreira (2005)

Publications Mathématiques de l'IHÉS

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We consider typical analytic unimodal maps which possess a chaotic attractor. Our main result is an explicit combinatorial formula for the exponents of periodic orbits. Since the exponents of periodic orbits form a complete set of smooth invariants, the smooth structure is completely determined by purely topological data (“typical rigidity”), which is quite unexpected in this setting. It implies in particular that the lamination structure of spaces of analytic unimodal maps (obtained...