Image Compression predicated on Recurrent Iterated Function Systems

某些随机共形迭代函数系统的计数问题

Counting Problem for Some Random Conformal Iterated Function Systems

本文研究随机共形迭代函数系统的计数问题，发现随机情形下计数性质与确定性系统根本不同，非指数增长可在满测度集上构造，且随机游走的常返行为起关键作用。

Analytic properties of hidden variable recurrent fractal interpolation function with function contractivity factors

In this paper, we analyze the smoothness and stability of hidden variable recurrent fractal interpolation functions (HVRFIF) with function contractivity factors introduced in Ref. 1. The HVRFIF is a hidden variable fractal interpolation function (HVFIF) constructed by recurrent iterated function system (RIFS) with function contractivity factors. An attractor of RIFS has a local self-similar or self-affine structure and looks more naturally than one of IFS. The contractivity factors of IFS(RIFS) determine fractal characteristic and shape of its attractor. Therefore, the HVRFIF with function con…

Construction of Fractal Surfaces by Recurrent Fractal Interpolation Curves

A method to construct fractal surfaces by recurrent fractal curves is provided. First we construct fractal interpolation curves using a recurrent iterated functions system(RIFS) with function scaling factors and estimate their box-counting dimension. Then we present a method of construction of wider class of fractal surfaces by fractal curves and Lipschitz functions and calculate the box-counting dimension of the constructed surfaces. Finally, we combine both methods to have more flexible constructions of fractal surfaces.

Absence of line fields and Mane's theorem for non-recurrent transcendental functions

Let f be a transcendental meromorphic function. Suppose that the finite part of the postsingular set of f is bounded, that f has no recurrent critical points or wandering domains, and that the degree of pre-poles of f is uniformly bounded. Then we show that f supports no invariant line fields on its Julia set. We prove this by generalizing two results about rational functions to the transcendental setting: a theorem of Mane about the branching of iterated preimages of disks, and a theorem of McMullen regarding absence of invariant line fields for "measurably transitive" functions. Both our the…

Estimation of errors on perturbation of function contractivity factors and box-counting dimension of hidden variable recurrent fractal interpolation function

In this paper, we study errors on perturbation of function contractivity factors and box-counting dimension of hidden variable recurrent fractal interpolation function (HVRFIF). The HVRFIF is a hidden variable fractal interpolation function (HVFIF) constructed by recurrent iterated function system (RIFS) with function contractivity factors. The contractivity factors of RIFS determine fractal characteristics and shape of its attractor, so that the HVRFIF with function contractivity factors has more flexibility and diversity than the HVFIF with constant contractivity factors. Stability of interp…

Non-hyperbolic Iterated Function Systems: attractors and stationary measures

We consider iterated function systems $\mathrm{IFS}(T_1,\dots,T_k)$ consisting of continuous self maps of a compact metric space $X$. We introduce the subset $S_{\mathrm{t}}$ of {\emph{weakly hyperbolic sequences}} $ξ=ξ_0\ldotsξ_n \ldots \in Σ_k^+$ having the property that $\bigcap_n T_{ξ_{0}}\circ\cdots\circ T_{ξ_{n}}(X)$ is a point $\{π(ξ)\}$. The target set $π(S_{\mathrm{t}})$ plays a role similar to the semifractal introduced by Lasota-Myjak. Assuming that $S_{\mathrm{t}}\ne \emptyset$ (the only hyperbolic-like condition we assume) we prove that the IFS has at most one strict attractor and…