Lifting Dynamical Properties to Hyperspaces
DOI:
https://doi.org/10.4995/agt.2014.1841Keywords:
transitivity, total transitivity, weakly mixing, mixing, topological exactness, topological conjugacy, Vietoris topology, hyperspace suspension.Abstract
For a dynamical system (X,f), the passage of various dynamical properties such as transitivity, total transitivity, weakly mixing, mixing, topological exactness, topological conjugacy, to the hyperspace C(X) of X consisting of nonempty closed connected subsets of X, and also to the hyperspace suspension HS(X) of X, have been considered and studied.
Downloads
References
J. Banks, Chaos for induced hyperspace maps, Chaos Solitons Fractals 25 (2005), 681-685.
(http://dx.doi.org/10.1016/j.chaos.2004.11.089)
J. J. Charatonik, Recent Research in Hyperspace Theory, Extracta Math. 18 (2003), 235-262.
R. L. Devaney, An introduction to chaotic dynamical systems, Redwood City, Addison-Wesley, 1989.
J. Dugundji, Topology, Allyn and Bacon, Boston, 1966.
R. Escobedo, M. López and S. Macias, On the hyperspace suspension of a continuum, Topology Appl. 138 (2004), 109-124.
(http://dx.doi.org/10.1016/j.topol.2003.08.024)
N. Esty, The hyperspaces $C_n(X)$ for finite ray-graphs, Appl. Gen. Topol. 14 (2013), 73-84.
J. L. G. Guirao, D. Kwietniak, M. Lampart, P. Oprocha and A. Peris, Chaos on hyperspaces, Nonlinear Anal. 71 (2009), 1-8.
(http://dx.doi.org/10.1016/j.na.2008.10.055)
S. Kolyada and L'. Snoha, Some aspects of topological transitivity - a survey, Grazer Math. Ber. 334 (1997), 3-35.
D. Kwietniak and P. Oprocha, Topological entropy and chaos for maps induced on hyperspaces, Chaos Solitons Fractals 33 (2007), 76-86.
(http://dx.doi.org/10.1016/j.chaos.2005.12.033)
S. B. Nadler, Hyperspaces of sets, M. Dekker, New York and Basel, 1978.
H. Roman-Flores, A note on transitivity in set-valued discrete systems, Chaos Solitons Fractals 17 (2003), 99-104.
(http://dx.doi.org/10.1016/S0960-0779(02)00406-X)
S. Ruette, Chaos for continuous interval maps, Universit$acute{e$ Paris-Sud, 91405 Orsay, Cedex - France (2003).
P. Sharma and A. Nagar, Topological dynamics on hyperspaces, Appl. Gen. Topol. 11 (2010), 1-19.
Downloads
Published
How to Cite
Issue
Section
License
This journal is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
