Hostname: page-component-77c89778f8-5wvtr Total loading time: 0 Render date: 2024-07-17T14:33:11.148Z Has data issue: false hasContentIssue false

ON GENERATORS AND DISTURBANCES OF DYNAMICAL SYSTEMS IN THE CONTEXT OF CHAOTIC POINTS

Published online by Cambridge University Press:  30 January 2019

RYSZARD J. PAWLAK
Affiliation:
Faculty of Mathematics and Computer Science, Łódź University, Banacha 22, 90-238 Łódź, Poland email ryszard.pawlak@wmii.uni.lodz.pl
JUSTYNA POPRAWA*
Affiliation:
Faculty of Mathematics and Computer Science, Łódź University, Banacha 22, 90-238 Łódź, Poland email justyna.poprawa@unilodz.eu

Abstract

We analyse local aspects of chaos for nonautonomous periodic dynamical systems in the context of generating autonomous dynamical systems and the possibility of disturbing them.

Type
Research Article
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alsedá, L., Llibre, J. and Misiurewicz, M., Combinatorial Dynamics and Entropy in Dimension One, 2nd edn (World Scientific, Singapore, 2000).Google Scholar
Blanchard, F., ‘Topological chaos: what may this mean?’, J. Differential Equations 15(1) (2009), 2346.Google Scholar
Block, L. S. and Coppel, W. A., Dynamics in One Dimension, Lecture Notes in Mathematics, 1513 (Springer, Berlin, 1992).Google Scholar
Engelking, R., General Topology (PWN Polish Sci. Publ., Warszawa, 1977).Google Scholar
Kolyada, S. and Snoha, L., ‘Topological entropy of nonautonomous dynamical systems’, Random Comput. Dyn. 4(2–3) (1996), 205233.Google Scholar
Korczak-Kubiak, E., Loranty, A. and Pawlak, R. J., ‘On points focusing entropy’, Entropy 20(2) (2018), Article ID, 11 pages.Google Scholar
Lee, J. M., Introduction to Topological Manifolds, Graduate Texts in Mathematics, 202 (Springer, New York, 2000).Google Scholar
Li, J. and Ye, X., ‘Recent development of chaos theory in topological dynamics’, Acta Math. Sin. (Engl. Ser.) 32(1) (2016), 83114.Google Scholar
Li, T. Y. and Yorke, J., ‘Period three implies chaos’, Amer. Math. Monthly 82 (1975), 985992.Google Scholar
Pawlak, R. J., ‘Distortion of dynamical systems in the context of focusing the chaos around the point’, Internat. J. Bifur. Chaos 28(1) (2018), Article ID 1850006, 13 pages.Google Scholar
Pawlak, R. J., Loranty, A. and Bąkowska, A., ‘On the topological entropy of continuous and almost continuous functions’, Topology Appl. 158 (2011), 20222033.Google Scholar
Ruette, S., Chaos on the Interval—A Survey of Relationship Between the Various Kinds of Chaos for Continuous Interval Maps, University Lecture Series, 67 (American Mathematical Society, Providence, RI, 2017).Google Scholar
Schweizer, B., Sklar, A. and Smital, J., ‘Distributional (and other) chaos and its measurement’, Real Anal. Exchange 26(2) (2000), 495524.Google Scholar