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@article{29850, author = {Tesarčík, Jan}, article_location = {Amsterdam}, article_number = {May}, doi = {http://dx.doi.org/10.1016/j.topol.2017.03.007}, keywords = {Dynamical system; Tree; Distributional functions; Spectrum; Weak spectrum; Basic omega-limit sets}, language = {eng}, issn = {0166-8641}, journal = {Topology and its Applications}, title = {On the spectrum of dynamical systems on trees}, url = {https://www.sciencedirect.com/science/article/pii/S0166864117301773}, volume = {222}, year = {2017} }
TY - JOUR ID - 29850 AU - Tesarčík, Jan PY - 2017 TI - On the spectrum of dynamical systems on trees JF - Topology and its Applications VL - 222 IS - May SP - 227-237 EP - 227-237 PB - Elsevier B.V. SN - 01668641 KW - Dynamical system KW - Tree KW - Distributional functions KW - Spectrum KW - Weak spectrum KW - Basic omega-limit sets UR - https://www.sciencedirect.com/science/article/pii/S0166864117301773 L2 - https://www.sciencedirect.com/science/article/pii/S0166864117301773 N2 - In their paper, Schweizer and Smital (1994) [10] introduced the notions of distributional chaos for continuous maps of the interval, spectrum and weak spectrum of a dynamical system. Among other things, they have proved that in the case of continuous interval maps, both the spectrum and the weak spectrum are finite and generated by points from the basic sets. Here we generalize the mentioned results for the case of continuous maps of a finite tree. While the results are similar, the original argument is not applicable directly and needs essential modifications. In particular, it was necessary to resolve the problem of intersection of basic sets, which was a crucial point. An example of one-dimensional dynamical system with an infinite spectrum is presented. ER -
TESARČÍK, Jan. On the spectrum of dynamical systems on trees. \textit{Topology and its Applications}. Amsterdam: Elsevier B.V., 2017, vol.~222, May, p.~227-237. ISSN~0166-8641. Available from: https://dx.doi.org/10.1016/j.topol.2017.03.007.
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