Paper Title:
Periodic Point at Real Axis for a Generalized 3x+1 Function
  Abstract

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, 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
$32.00
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