A discrete chaotic dynamical system on the Sierpinski gasket

Öz The Sierpinski gasket (also known as the Sierpinski triangle) is one of the fundamental models of self-similar sets. There have been many studies on different features of this set in the last decades. In this paper, initially we construct a dynamical system on the Sierpinski gasket by using expanding and folding maps. We then obtain a surprising shift map on the code set of the Sierpinski gasket, which represents the dynamical system, and we show that this dynamical system is chaotic on the code set of the Sierpinski gasket with respect to the intrinsic metric. Finally, we provide an algorithm to compute periodic points for this dynamical system.

Kaynak Göster

Bibtex @ { tbtkmath575268, journal = {Turkish Journal of Mathematics}, issn = {1300-0098}, eissn = {1303-6149}, address = {}, publisher = {TÜBİTAK}, year = {2019}, volume = {43}, pages = {361 - 372}, doi = {}, title = {A discrete chaotic dynamical system on the Sierpinski gasket}, key = {cite}, author = {Saltan, Mustafa and Aslan, Nisa and Demir, Bünyamin} }
APA Saltan, M , Aslan, N , Demir, B . (2019). A discrete chaotic dynamical system on the Sierpinski gasket . Turkish Journal of Mathematics , 43 (1) , 361-372 .
MLA Saltan, M , Aslan, N , Demir, B . "A discrete chaotic dynamical system on the Sierpinski gasket" . Turkish Journal of Mathematics 43 (2019 ): 361-372 <
Chicago Saltan, M , Aslan, N , Demir, B . "A discrete chaotic dynamical system on the Sierpinski gasket". Turkish Journal of Mathematics 43 (2019 ): 361-372
RIS TY - JOUR T1 - A discrete chaotic dynamical system on the Sierpinski gasket AU - Mustafa Saltan , Nisa Aslan , Bünyamin Demir Y1 - 2019 PY - 2019 N1 - DO - T2 - Turkish Journal of Mathematics JF - Journal JO - JOR SP - 361 EP - 372 VL - 43 IS - 1 SN - 1300-0098-1303-6149 M3 - UR - Y2 - 2021 ER -
EndNote %0 Turkish Journal of Mathematics A discrete chaotic dynamical system on the Sierpinski gasket %A Mustafa Saltan , Nisa Aslan , Bünyamin Demir %T A discrete chaotic dynamical system on the Sierpinski gasket %D 2019 %J Turkish Journal of Mathematics %P 1300-0098-1303-6149 %V 43 %N 1 %R %U
ISNAD Saltan, Mustafa , Aslan, Nisa , Demir, Bünyamin . "A discrete chaotic dynamical system on the Sierpinski gasket". Turkish Journal of Mathematics 43 / 1 (Şubat 2019): 361-372 .
AMA Saltan M , Aslan N , Demir B . A discrete chaotic dynamical system on the Sierpinski gasket. Turkish Journal of Mathematics. 2019; 43(1): 361-372.
Vancouver Saltan M , Aslan N , Demir B . A discrete chaotic dynamical system on the Sierpinski gasket. Turkish Journal of Mathematics. 2019; 43(1): 361-372.
IEEE M. Saltan , N. Aslan ve B. Demir , "A discrete chaotic dynamical system on the Sierpinski gasket", Turkish Journal of Mathematics, c. 43, sayı. 1, ss. 361-372, Şub. 2019