On distributional spectrum of piecewise monotonic maps

@article{67561,
   author = {Tesarčík, Jan and Pravec, Vojtěch},
   article_location = {Basel},
   article_number = {1},
   doi = {http://dx.doi.org/10.1007/s00010-022-00913-2},
   keywords = {Omega-limit set; Distributional chaos; Spectrum of distributional functions; Piecewise monotonic maps},
   language = {eng},
   issn = {0001-9054},
   journal = {Aequationes Mathematicae},
   title = {On distributional spectrum of piecewise monotonic maps},
   url = {https://link.springer.com/article/10.1007/s00010-022-00913-2},
   volume = {97},
   year = {2023}
}

TY  - JOUR
ID  - 67561
AU  - Tesarčík, Jan - Pravec, Vojtěch
PY  - 2023
TI  - On distributional spectrum of piecewise monotonic maps
JF  - Aequationes Mathematicae
VL  - 97
IS  - 1
SP  - 133-145
EP  - 133-145
PB  - Birkhauser Verlag AG
SN  - 00019054
KW  - Omega-limit set
KW  - Distributional chaos
KW  - Spectrum of distributional functions
KW  - Piecewise monotonic maps
UR  - https://link.springer.com/article/10.1007/s00010-022-00913-2
N2  - 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.
ER  - 

TESARČÍK, Jan and Vojtěch PRAVEC. On distributional spectrum of piecewise monotonic maps. \textit{Aequationes Mathematicae}. Basel: Birkhauser Verlag AG, 2023, vol.~97, No~1, p.~133-145. ISSN~0001-9054. Available from: https://dx.doi.org/10.1007/s00010-022-00913-2.