Uniformly recurrent sequences and minimal Cantor omega-limit sets

• Autorzy: Lori Alvin
• Języki publikacji: EN

Abstrakty

EN

We investigate the structure of kneading sequences that belong to unimodal maps for which the omega-limit set of the turning point is a minimal Cantor set. We define a scheme that can be used to generate uniformly recurrent and regularly recurrent infinite sequences over a finite alphabet. It is then shown that if the kneading sequence of a unimodal map can be generated from one of these schemes, then the omega-limit set of the turning point must be a minimal Cantor set.

Kategorie tematyczne

• 54H20: Topological dynamics
• 37B10: Symbolic dynamics
• 37B20: Notions of recurrence
• 37E05: Maps of the interval (piecewise continuous, continuous, smooth)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 231
• Numer: 3
• Strony: 273-284

Daty

wydano

2015

Twórcy

autor

Lori Alvin

• Department of Mathematics, Bradley University, 1501 W. Bradley Ave., Peoria, IL 61625, U.S.A.

Identyfikatory

DOI

10.4064/fm231-3-3