On expansive chaotic maps in G-spaces
About this article
Abstract
In this paper we define expansive maps in general topological space (not necessarily metrizable space) and generalize this definition to G-spaces and give some propertie of such maps. Also we study some properties of new type of chaotic maps which we called G-expansive chaotic maps.
Keywords: G- Periodic Points, G-Orbits, G-Expansive Maps, G-Expansive Chaos.
References
[1] Aoki, N. and Hiraide, K. Topological Theory of Dynamical Systems. , North Holland Mathematical Library, North-Holland, Amsterdam (1994).
[2] Arhangel'skii, A. and Tkachenko, M. Topological Groups and Related Structures, Atlantis Press, World Scientific, (2008).
[3] Choi, T.and Kim, J. Decomposition Theorem on G-Spaces. , Osaka Journal of the Indian Mathematical, 46(2009), no.1, 87-104.
[4] Das, R.Expansive self-homeomorphism on G-Spaces. , Periodica Math.Hungarica, 31(1995), 123-130.
[5] Das, R. .On G-Expansive Homeomorphisms and Generators, the Journalof the Indian Mathematical Society. New Series, 72(2005), no., 1-4, 83-89.
View more references (14)
[6] Das, R. And Das, T. .Topological Transitive of Uniform Limit Function on G-Spaces, The Journal of Mathematical Analysis, 6 (2012), no.29-32, 1491-1499.
[7] Das, R. and Das, T.Chaos of Product Map on G-Spaces, Int. Journal of Math. Forum, 8(2013), no.13, 647-652.
[8] Das, R. and Das, T. .A note on Representation of Pseudovariant Maps., Math. Solvaca 62(2012).no.1, 137-142.
[9] Das, R. and Das, T.On Properties of G-Expansive Homeomorpisms. , Math. Solvaca62 (2012).no.3, 531-538.
[10] Das, R. and Das, T.On Extension of G-Expansive Homeomorpisms, the Journal of the Indian Mathematical Society. New Series, 67(2000), no.1-4, 35-41.
[11] Devaney, R.L. An Introduction to Chaotic Dynamical Systems. , Addison-Wesley, 1989.
[12] Gottschalk,W. and Hedlund,G. .Topological Dynamics. , Amer, Math, Soci(1955) .
[13] Husain, T.Introduction toTopological groups. , W.B. Saunders Company Philadelphia And London (1966) .
[14] Kumar, V.On Chaotic and Fractals in General Topological Spaces., P.H.D. Cochin University of Science and Technology under Faculty of Science. 2001.
[15] Richeson, D. and Wiseman, J.Positive Expansive Homeomorphisms of Compact Spaces, IJMS 54(2004), 2907-2910.
[16] Shah,E. and Das, T. .Consequence of Shadowing Property ofG-Spaces. ,Int.Journal of Math. Analysis, 7(2013), no.12, 579-588.
[17] Shah, E. and Das, T.On Pseudo Orbit tracing Property of G-Spaces. , JP Journal of Geometry and Topology, 3(2003), no.2, 101-112.
[18] Utz,, W.R. .Unstable Homeomorphism. Proceedings of the American Mathematical Society, 1(1950), 769-774.
[19] Willard, S. General Topology. , Addison-Westy Pub.co, Inc.1970.