The Dynamical System Generated by the 3n+1 Function
Author:   Günther J. Wirsching
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Volume:   1681
ISBN:  

9783540639701


Pages:   164
Publication Date:   19 February 1998
Format:   Paperback
Availability:   Out of print, replaced by POD   Availability explained
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The Dynamical System Generated by the 3n+1 Function


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Overview

The 3n+1 function T is defined by T(n)=n/2 for n even, and T(n)=(3n+1)/2 for n odd. The famous 3n+1 conjecture, which remains open, states that, for any starting number n>0, iterated application of T to n eventually produces 1. After a survey of theorems concerning the 3n+1 problem, the main focus of the work is 3n+1 predecessor sets. These are analyzed using, for example, elementary number theory, combinatorics, asynptotic analysis, and abstract measure theory. The book is written for any mathematician interested in the 3n+1 problem, and in the wealth of mathematical ideas employed to attack it.

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