The Dynamical System Generated by the 3n+1 Function

by Günther J. Wirsching

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 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.

Product Details

ISBN-13:	9783540639701
Publisher:	Springer Berlin Heidelberg
Publication date:	03/20/1998
Series:	Lecture Notes in Mathematics , #1681
Edition description:	1998
Pages:	164
Product dimensions:	8.50(w) x 10.98(h) x 0.01(d)

Table of Contents

Some ideas around 3n+1 iterations.- Analysis of the Collatz graph.- 3-adic averages of counting functions.- An asymptotically homogeneous Markov chain.- Mixing and predecessor density.