A family of chaotic dynamical systems on the Cantor dust C x C
Open Access
- 1 January 2023
- journal article
- research article
- Published by National Library of Serbia in Filomat
- Vol. 37 (6) , 1915-1925
Abstract
In this paper, we give a family of dynamical systems on the Cantor dust (Cx C) by using elements of 4th Dihedral group with shift map and then express them via code representations of the points of C x C. Moreover, we prove that these systems are chaotic in the sense of Devaney and also we investigate the topological equivalence of these dynamical systems.Keywords
This publication has 17 references indexed in Scilit:
- A discrete chaotic dynamical system on the Sierpinski gasketTURKISH JOURNAL OF MATHEMATICS, 2019
- An explicit formula of the intrinsic metric on the Sierpinski gasket via code representationTURKISH JOURNAL OF MATHEMATICS, 2018
- Encounters with Chaos and Fractals2012
- Measure, Topology, and Fractal Geometry2008
- Chaos and Fractals2004
- Fractal Geometry2003
- A note on positive Lyapunov exponent and sensitive dependence on initial conditionsChaos, Solitons & Fractals, 2001
- Analysis on Fractals2001
- Chaos1996
- Smale’s Horseshoe Map via Ternary NumbersSIAM Review, 1994