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

Abstract:

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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.

Info:

Periodical:

Edited by:

Qi Luo

Pages:

1341-1345

DOI:

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

Citation:

S. Liu et al., "The Existence of Fixed Point for a Generalized 3x+1 Function", Applied Mechanics and Materials, Vols. 55-57, pp. 1341-1345, 2011

Online since:

May 2011

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Price:

$35.00

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