J 2023

On distributional spectrum of piecewise monotonic maps

TESARČÍK, Jan and Vojtěch PRAVEC

Basic information

Original name

On distributional spectrum of piecewise monotonic maps

Authors

TESARČÍK, Jan (203 Czech Republic, guarantor, belonging to the institution) and Vojtěch PRAVEC (203 Czech Republic, belonging to the institution)

Edition

Aequationes Mathematicae, Basel, Birkhauser Verlag AG, 2023, 0001-9054

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Switzerland

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

RIV identification code

RIV/47813059:19610/23:A0000133

Organization unit

Mathematical Institute in Opava

DOI

UT WoS

000854419800001

Keywords in English

Omega-limit set; Distributional chaos; Spectrum of distributional functions; Piecewise monotonic maps

Tags

Tags

International impact, Reviewed
Změněno: 27/3/2024 14:50, Mgr. Aleš Ryšavý

Abstract

V originále

We study a certain class of piecewise monotonic maps of an interval. These maps are strictly monotone on finite interval partitions, satisfy the Markov condition, and have generator property. We show that for a function from this class distributional chaos is always present and we study its basic properties. The main result states that the distributional spectrum, as well as the weak spectrum, is always finite. This is a generalization of a similar result for continuous maps on the interval, circle, and tree. An example is given showing that conditions on the mentioned class can not be weakened.