A classification of inverse limit spaces of tent maps with finite critical orbit

Štimac, Sonja

doi:10.1016/j.topol.2007.03.003

Cited by 16 publications

(21 citation statements)

References 11 publications

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“…Let us denote by ℓ x p a link of C p which contains the point x. From [19] and [2] (for the finite and infinite critical orbit case, respectively) we have the following proposition: From [6,7] and [10] we can derive of the chain C p . Using this notation we can write Proposition 3.1 in the following way: h(x) ≈ p σ R (x) for every x ∈ E q .…”

Section: Construction Of Chains C P and C P+mmentioning

confidence: 99%

Entropy of homeomorphisms on unimodal inverse limit spaces

Bruin

Štimac

2013

Nonlinearity

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We prove that every self-homeomorphism h : K s → K s on the inverse limit space K s of the tent map T s with slope s ∈ ( √ 2, 2] has topological entropy h top (h) = |R| log s, where R ∈ Z is such that h and σ R are isotopic. Conclusions on the possible values of the entropy of homeomorphisms of the inverse limit space of a (renormalizable) quadratic map are drawn as well.2000 Mathematics Subject Classification. 54H20, 37B45, 37E05.

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Section: Construction Of Chains C P and C P+mmentioning

confidence: 99%

Entropy of homeomorphisms on unimodal inverse limit spaces

Bruin

Štimac

2013

Nonlinearity

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“…The result of Kailhofer has been substantially improved. Stimac [38] has shown that if the forward orbit of c is finite, then Ingram's Conjecture holds for those s. This, of course, includes the case that the forward orbit of c is periodic. Another result has been announced by Raines and Stimac dealing with the case that the critical point c is non-recurrent.…”

Section: Discussionmentioning

confidence: 99%

Attractors and inverse limits

Keesling

2008

Rev. R. Acad. Cien. Serie A. Mat.

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This paper surveys some recent results concerning inverse limits of tent maps. The survey concentrates on Ingram's Conjecture. Some motivation is given for the study of such inverse limits. Atractores y límites inversosResumen. Este artículo expone algunos resultados recientes sobre límites inversos de aplicaciones tienda. La exposición se concentra en la Conjetura de Ingram. Se presentan tambien algunas motivaciones para el estudio de tales límites inversos.

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“…It is easy to see that p -bridges are p -symmetric, and that L p OEx B determines the q -folding pattern of the p -bridge B , for all q Ä p (see Lemma 3.8 in [29]). …”

Section: Preliminariesmentioning

confidence: 99%

“…Now we recall the definition of a family of chains of K s introduced in [29]. Let V n be the set of all allowed sequences of length n ordered by the parity-lexicographical ordering.…”

Section: Remark 218mentioning

confidence: 99%