Periodic Point at Real Axis for a Generalized 3x+1 Function

Abstract:

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In order to study the fractal character of representative complex exponential function just as generalized 3x+1 function T(x). In this essay, we proved that T(x) has periodic points of every period in bound (n, n+1) when n>1 in real axis. Then, we found the distribution of 2-periods points of T(x) in real axis. We put forward the bottom bound of 2-periodic point’s number and proved it. Moreover, we found the number of T(x)’s 2-periodic points in different bounds to validate our conclusion. Then, we extended the conclusion to i-periods points and find similar conclusion. Finally, we proved there exist endless convergence and divergence points of T(x) in real axis.

Info:

Periodical:

Edited by:

Qi Luo

Pages:

1670-1674

DOI:

10.4028/www.scientific.net/AMM.55-57.1670

Citation:

S. Liu and Z. X. Wang, "Periodic Point at Real Axis for a Generalized 3x+1 Function", Applied Mechanics and Materials, Vols. 55-57, pp. 1670-1674, 2011

Online since:

May 2011

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Price:

$35.00

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