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The Dynamical System Generated by the 3n+1 Function

  • Book
  • © 1998

Overview

Authors:
  1. Günther J. Wirsching
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1681)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-vii
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  2. Introduction

    • G. J. Wirsching
    Pages 1-9

  3. Some ideas around 3n+1 iterations

    • Günther J. Wirsching
    Pages 10-30

  4. Analysis of the Collatz graph

    • Günther J. Wirsching
    Pages 31-75

  5. 3-adic averages of counting functions

    • Günther J. Wirsching
    Pages 76-95

  6. An asymptotically homogeneous Markov chain

    • Günther J. Wirsching
    Pages 96-122

  7. Mixing and predecessor density

    • Günther J. Wirsching
    Pages 123-140

  8. Back Matter

    Pages 141-158
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: The Dynamical System Generated by the 3n+1 Function

  • Authors: Günther J. Wirsching

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0095985

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1998

  • Softcover ISBN: 978-3-540-63970-1Published: 19 February 1998

  • eBook ISBN: 978-3-540-69677-3Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 164

  • Topics: Number Theory, Theory of Computation

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