Lifting Dynamical Properties to Hyperspaces

Dania Masood, Pooja Singh

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.

 


Keywords

transitivity; total transitivity; weakly mixing; mixing; topological exactness; topological conjugacy; Vietoris topology; hyperspace suspension.

Subject classification

54H20; 37B99.

Full Text:

PDF

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.

Abstract Views

4272
Metrics Loading ...

Metrics powered by PLOS ALM




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