Abstract
There is a natural relationship between fractals and chaos. In addition, different chaotic dynamical systems can be defined depending on the structure of the relevant fractal. In this paper, we first define a family of dynamical systems on the discrete Sierpinski triangle by using the composition of the shift map and the elements of S3, which is the group of symmetries of the equilateral triangle, via the code representations of the points. Moreover, we give a general formula to construct different dynamical systems on this fractal. Thus, we obtain a family of dynamical systems which are Devaney chaotic. Finally, we classify these dynamical systems in term of topological conjugacy.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
