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@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.
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