The Dynamical System Generated by the 3n+1 Function

By Günther J. Wirsching

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 book are 3n+1 predecessor sets. These are analyzed using, e.g., elementary number theory, combinatorics, asymptotic 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.

• Format: Paperback
• Language: English
• ISBN: 3540639705
• ISBN13: 9783540639701
• Release Date: February 1998
• Publisher: Springer
• Length: 164 Pages
• Weight: 0.56 lbs.
• Dimensions: 0.4" x 6.1" x 9.2"