Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
10.22034/kjm.2022.367135.2696
Abstract
The orbit of a point $x\in X$ in a classical iterated function system (IFS) can be defined as $\{f_u(x)=f_{u_n}\circ\cdots \circ f_{u_1}(x):$ $u=u_1\cdots u_n$ is a word of a full shift $\Sigma$ on finite symbols and $f_{u_i}$ is a continuous self map on $X \}$. One also can associate to $\sigma=\sigma_1\sigma_2\cdots\in\Sigma$ a non-autonomous system $(X,\,f_\sigma)$ where the trajectory of $x\in X$ is defined as $x,\,f_{\sigma_1}(x),\,f_{\sigma_1\sigma_2}(x),\ldots$. Here instead of the full shift, we consider an arbitrary shift space $\Sigma$. Then we investigate basic properties related to this IFS and the associated non-autonomous systems. In particular, we look for sufficient conditions that guarantees that in a transitive IFS one may have a transitive $(X,\,f_\sigma)$ for some $\sigma\in\Sigma$ and how abundance are such $\sigma$'s.
Aghaee, M., & Ahmadi Dastjerdi, D. (2023). Iterated function systems over arbitrary shift spaces. Khayyam Journal of Mathematics, 9(1), 127-143. doi: 10.22034/kjm.2022.367135.2696
MLA
Mahdi Aghaee; Dawoud Ahmadi Dastjerdi. "Iterated function systems over arbitrary shift spaces". Khayyam Journal of Mathematics, 9, 1, 2023, 127-143. doi: 10.22034/kjm.2022.367135.2696
HARVARD
Aghaee, M., Ahmadi Dastjerdi, D. (2023). 'Iterated function systems over arbitrary shift spaces', Khayyam Journal of Mathematics, 9(1), pp. 127-143. doi: 10.22034/kjm.2022.367135.2696
VANCOUVER
Aghaee, M., Ahmadi Dastjerdi, D. Iterated function systems over arbitrary shift spaces. Khayyam Journal of Mathematics, 2023; 9(1): 127-143. doi: 10.22034/kjm.2022.367135.2696
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