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
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
RIV identification code
RIV/47813059:19610/23:A0000133
Organization unit
Mathematical Institute in Opava
Keywords in English
Omega-limit set; Distributional chaos; Spectrum of distributional functions; Piecewise monotonic maps
Tags
International impact, Reviewed
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.
Displayed: 24/12/2024 13:13