Transversal family of non-autonomous conformal iterated function systems

  • Yuto Nakajima

    Keio University, Yokohama, Japan
Transversal family of non-autonomous conformal iterated function systems cover
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Abstract

We study Non-autonomous Iterated Function Systems (NIFSs) with overlaps. A NIFS on a compact subset is a sequence of collections of uniformly contracting maps , where is a finite set. In comparison to usual iterated function systems, we allow the contractions applied at each step to depend on . In this paper, we focus on a family of parameterized NIFSs on . Here, we do not assume the open set condition. We show that if a -parameter family of such systems satisfies the transversality condition, then for almost every parameter value the Hausdorff dimension of the limit set is the minimum of and the Bowen dimension. Moreover, we give an example of a family of parameterized NIFSs such that satisfies the transversality condition but does not satisfy the open set condition for any .

Cite this article

Yuto Nakajima, Transversal family of non-autonomous conformal iterated function systems. J. Fractal Geom. 11 (2024), no. 1/2, pp. 57–84

DOI 10.4171/JFG/144