Topological mixing, knot points and bounds of topological entropy

Piotr Oprocha; Paweł Potorski

doi:10.3934/dcdsb.2015.20.3547

Article Contents

2015, Volume 20, Issue 10: 3547-3564. Doi: 10.3934/dcdsb.2015.20.3547

This issue Previous Article Directional uniformities, periodic points, and entropy Next Article Projective distance and $g$-measures

Topological mixing, knot points and bounds of topological entropy

Piotr Oprocha^1, and
Paweł Potorski^2,

1.
Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków
2.
AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow

Received: November 30, 2014

Revised: February 28, 2015

Published: November 2015

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Abstract

In the paper we provide exact lower bounds of topological entropy in the class of transitive and mixing maps preserving the Lebesgue measure which are nowhere monotone (with dense knot points).

Keywords:

Mathematics Subject Classification: Primary: 37B40; Secondary: 37E05, 37A05.

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