All but one expanding Lorenz maps with slope greater than or equal to $\sqrt 2$ are leo

Piotr Bartłomiejczyk; Piotr Nowak-Przygodzki

doi:10.4064/cm9382-10-2024

All but one expanding Lorenz maps with slope greater than or equal to $\sqrt 2$ are leo

Abstract

We prove that with only one exception, all expanding Lorenz maps $f\colon[0,1]\to[0,1]$ with the derivative $f'(x)\ge\sqrt{2}$ (apart from a finite set of points) are locally eventually onto. Namely, for each such $f$ and each nonempty open interval $J\subset(0,1)$ there is $n\in\N$ such that $[0,1)\subset f^n(J)$. The mentioned exception is the map $f_0(x)=\sqrt{2}x+(2-\sqrt{2})/2 \pmod 1$. Recall that $f$ is an expanding Lorenz map if it is strictly increasing on $[0,c)$ and $[c,1]$ for some $c$ and satisfies the condition $\inf{f'}>1$.

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Authors (2)

Piotr Bartłomiejczyk dr hab.
Piotr Nowak-Przygodzki

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Articles

Type:

artykuły w czasopismach

Published in:

Colloquium Mathematicum pages 193 - 206,
ISSN: 0010-1354

Language:

English

Publication year:

2024

Bibliographic description:

Bartłomiejczyk P., Nowak-Przygodzki P.: All but one expanding Lorenz maps with slope greater than or equal to $\sqrt 2$ are leo// Colloquium Mathematicum -Vol. 176,iss. 2 (2024), s.193-206

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