The Dynamical System Generated by the 3n+1 Function / Edition 1

The Dynamical System Generated by the 3n+1 Function / Edition 1

by Gunther J. Wirsching
     
 

ISBN-10: 3540639705

ISBN-13: 9783540639701

Pub. Date: 03/20/1998

Publisher: Springer Berlin Heidelberg

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,

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 Series, #1681
Edition description:
1998
Pages:
164
Product dimensions:
9.21(w) x 6.14(h) x 0.38(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.

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