Fractal and Hausdorff dimensions for systems of iterative functional equations

[摘要] We consider systems of non-affine iterative functional equations. From the constructive form of the solutions, recently established by the authors, representations of these systems in terms of symbolic spaces as well as associated fractal structures are constructed. These results are then used to derive upper bounds both for the appropriate fractal dimension and the corresponding Hausdorff dimension of solutions. Using the formalism of iterated function systems, we obtain a sharp result on the Hausdorff dimension in terms of the corresponding fractal structures. The connections of our results with related objects known in the literature, including Girgensohn functions, fractal interpolation functions and Weierstrass functions, are established. (C) 2019 Elsevier Inc. All rights reserved.

[发布日期] 2019-12-15

[关键词] Fractal structure;Hausdorff dimension;Fractal dimension;Symbolic space;Fractal interpolation function;System of iterative functional equations