The Existence of Fixed Point for a Generalized 3x+1 Function

Shuai Liu; Xiang Jiu Che; Zheng Xuan Wang

doi:10.4028/www.scientific.net/AMM.55-57.1341

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 55-57The Existence of Fixed Point for a Generalized...

The Existence of Fixed Point for a Generalized 3x+1 Function

Abstract:

In order to study generalized 3x+1 function C(z), we find the character of fixed points of C(z) at real axis by complex analytical analysis. Then we improve the solving algorithm of its fixed points. We proved that the integer fixed points of C(z) are 0 and -1 and the attract fixed points of C(z) are 0 and -1.2777. Popularized the result to complex plane, we prove that there is no fixed point of C(z) except real axis. We draw the fractal figures of C(z) by escape time algorithm to prove the result and give a conjecture from the fractal figures. The conjecture guess that the attract domain of C(z) is a connected domain which is connected with single point.

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Periodical:

Applied Mechanics and Materials (Volumes 55-57)

Pages:

1341-1345

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.55-57.1341

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Online since:

May 2011

Authors:

Shuai Liu, Xiang Jiu Che, Zheng Xuan Wang

Keywords:

Attractive Fixed Point, Escape Time, Fixed Point, Fractal, Generalized 3x+1 Function

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