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The Dynamical System Generated by the 3n+1 Function

  • Authors
  • Günther J. Wirsching

Part of the Lecture Notes in Mathematics book series (LNM, volume 1681)

Table of contents

  1. Front Matter
    Pages i-vii
  2. G. J. Wirsching
    Pages 1-9
  3. Günther J. Wirsching
    Pages 10-30
  4. Günther J. Wirsching
    Pages 31-75
  5. Günther J. Wirsching
    Pages 76-95
  6. Günther J. Wirsching
    Pages 96-122
  7. Günther J. Wirsching
    Pages 123-140
  8. Back Matter
    Pages 141-158

About this book

Introduction

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.

Keywords

3n+1 problem asymptotic analysis calculus collatz graph dynamical systems on N number theory p-adic distribution

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0095985
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-63970-1
  • Online ISBN 978-3-540-69677-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site