Displaying similar documents to “Structure of inverse limit spaces of tent maps with finite critical orbit”

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.

Inverse limits of tentlike maps on trees

Stewart Baldwin (2010)

Fundamenta Mathematicae

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We investigate generalizations of Ingram's Conjecture involving maps on trees. We show that for a class of tentlike maps on the k-star with periodic critical orbit, different maps in the class have distinct inverse limit spaces. We do this by showing that such maps satisfy the conclusion of the Pseudo-isotopy Conjecture, i.e., if h is a homeomorphism of the inverse limit space, then there is an integer N such that h and σ̂^N switch composants in the same way, where σ̂ is the standard...

Adding machines, endpoints, and inverse limit spaces

Lori Alvin, Karen Brucks (2010)

Fundamenta Mathematicae

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Let f be a unimodal map in the logistic or symmetric tent family whose restriction to the omega limit set of the turning point is topologically conjugate to an adding machine. A combinatoric characterization is provided for endpoints of the inverse limit space (I,f), where I denotes the core of the map.

On the ∗-product in kneading theory

Karen Brucks, R. Galeeva, P. Mumbrú, D. Rockmore, Charles Tresser (1997)

Fundamenta Mathematicae

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We discuss a generalization of the *-product in kneading theory to maps with an arbitrary finite number of turning points. This is based on an investigation of the factorization of permutations into products of permutations with some special properties relevant for dynamics on the unit interval.