Induced dynamics on the hyperspaces
In this paper, we study the dynamics induced by finite commutative relation on the hyperspaces. We prove that the dynamics induced on the hyperspace by a non-trivial commutative family of continuous self maps cannot be transitive and hence cannot exhibit higher degrees of mixing. We also prove that the dynamics induced on the hyperspace by such a collection cannot have dense set of periodic points. We also give example to show that the induced dynamics in this case may or may not be sensitive.
J. Banks, Chaos for induced hyperspace maps, Chaos, Solitons and Fractals 25 (2005), 681-685. https://doi.org/10.1016/j.chaos.2004.11.089
G. Beer, Topologies on Closed and Closed Convex Sets, Kluwer Academic Publishers, Dordrecht/Boston/London (1993). https://doi.org/10.1007/978-94-015-8149-3
L. Block and W. Coppel, Dynamics in one dimension, Springer-Verlag, Berlin Hiedelberg (1992). https://doi.org/10.1007/BFb0084762
M. Brin and G. Stuck, Introduction to dynamical systems, Cambridge Unversity Press (2002). https://doi.org/10.1017/CBO9780511755316
R. L. Devaney, Introduction to chaotic dynamical systems, Addisson Wesley (1986).
R. Klaus and P. Rohde, Fuzzy chaos : Reduced chaos in the combined dynamics of several independently chaotic populations, The American Naturalist 158, no. 5 (2001), 553-556. https://doi.org/10.1086/323120
D. Kwietniak and P. Oprocha, Topological entropy and chaos for maps induced on hyperspaces, Chaos Solitions
E. Micheal, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71(1951), 152-82. https://doi.org/10.1090/S0002-9947-1951-0042109-4
G. Di Maio and S. Naimpally, Some notes on hyperspace topologies. Ricerche Mat. 51, no. 1 (2002), 49-60.
A. Nagar and P. Sharma, Combined dynamics on hyperspaces, Topology Proceedings 38 (2011), 399-410.
S. Naimpally, All hypertopologies are hit-and-miss, Appl. Gen. Topol. 3, no. 1 (2002), 45-53. https://doi.org/10.4995/agt.2002.2111
S. Dirren and H. Davies, Combined dynamics of boundary and interior perturbations in the Eady setting, Journal of the atmospheric Sciences 61 (13) (2004), 1549-1565. https://doi.org/10.1175/1520-0469(2004)061<1549:CDOBAI>2.0.CO;2
P. Sharma and A. Nagar, Topological dynamics on hyperspaces, Appl. Gen. Topol. 11, no. 1 (2010), 1-19. https://doi.org/10.3366/nor.2010.0001
P. Sharma and A. Nagar, Inducing sensitivity on hyperspaces, Topology and its Applications 157 (2010), 2052-2058. https://doi.org/10.1016/j.topol.2010.05.002
J. P. Switkes, E. J. Rossettter, I. A. Co and J. C. Gerdes, Handwheel force feedback for lanekeeping assistance: combined dynamics and stability, Journal of Dynamic systems, Measurement and control 128, no. 3 (2006), 532-542. https://doi.org/10.1115/1.2229256
H. Roman-Flores, A note on transitivity in set valued discrete systems, Chaos, Solitons and Fractals, 17 (2003),99-104. https://doi.org/10.1016/S0960-0779(02)00406-X
Y. Zhao, S. Yokojima and G. Chen, Reduced density matrix and combined dynamics of electron and nuclei, Journal of Chemical Physics 113, no. 10 (2000), 4016-4027. https://doi.org/10.1063/1.1288374
Metrics powered by PLOS ALM
Cited-By (articles included in Crossref)
This journal is a Crossref Cited-by Linking member. This list shows the references that citing the article automatically, if there are. For more information about the system please visit Crossref site
1. Topological dynamics of Nondeterministic Cellular Automata
Pietro Di Lena
Information and Computation vol: 274 first page: 104532 year: 2020
Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.
Universitat Politècnica de València
e-ISSN: 1989-4147 https://doi.org/10.4995/agt