http://popups.lib.uliege.be/1373-5411/index.php?id=2086 Publications of Auteurs Takeshi Yoshikawa fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=2713 In this paper, we deal with the parameter dependency for the limit figures and the sufficient number of iterations in drawing the limit figures of quadratic transformations. The structure of the limit figures depends on the coefficients of the transformation, and has turned out to be complicated. Using the property that the limit figures are one-way functions, Da-te (2001) proposed an authentication algorithm. For the purpose of verification of the securities in the authentication algorithm, we show the experimental results for some properties of the limit figures. Fri, 30 Aug 2024 11:54:24 +0200 Fri, 30 Aug 2024 11:54:33 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2713 http://popups.lib.uliege.be/1373-5411/index.php?id=2080 In this paper, we deal with intuitively simple properties of the limit figures of two-dimensional inhomogeneous quadratic transformations. The divergence-convergence boundary of homogeneous quadratic transformations was investigated in detail in Da-te (1978). In an inhomogeneous case, there exist, possibly, the region of initial points converging to a fixed point other than the origin due to the linear terms. Then, there appears a boundary with a finite area as a limit figure. Next, in certain cases, the convergence regions or the divergence regions consist of infinite number of separated regions. We show the examples of the properties, and investigate them. Mon, 29 Jul 2024 11:29:00 +0200 Mon, 29 Jul 2024 11:29:15 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2080