An Intuitively Simple Property of Limit Figures of Quadratic Transformations
p. 413-420
Résumé
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.
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Référence papier
Takeshi Yoshikawa, Tsutomu Da-te et Hidetoshi Nonaka, « An Intuitively Simple Property of Limit Figures of Quadratic Transformations », CASYS, 11 | 2002, 413-420.
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Takeshi Yoshikawa, Tsutomu Da-te et Hidetoshi Nonaka, « An Intuitively Simple Property of Limit Figures of Quadratic Transformations », CASYS [En ligne], 11 | 2002, mis en ligne le 29 July 2024, consulté le 20 September 2024. URL : http://popups.lib.uliege.be/1373-5411/index.php?id=2080
Auteurs
Takeshi Yoshikawa
Division of Systems and Information Engineering, Hokkaido University, Kita 13, Nishi 8, Kita-ku, Sapporo, 060-8628, Japan
Tsutomu Da-te
Division of Systems and Information Engineering, Hokkaido University, Kita 13, Nishi 8, Kita-ku, Sapporo, 060-8628, Japan
Hidetoshi Nonaka
Division of Systems and Information Engineering, Hokkaido University, Kita 13, Nishi 8, Kita-ku, Sapporo, 060-8628, Japan