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Lecture Notes in Mathematics

The Dynamical System Generated by the 3n+1 Function

Authors: Wirsching, Günther J.

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  • ISBN 978-3-540-69677-3
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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.

Table of contents (6 chapters)

Table of contents (6 chapters)
  • Introduction

    Pages 1-9

    Wirsching, G. J.

  • Some ideas around 3n+1 iterations

    Pages 10-30

    Wirsching, Günther J.

  • Analysis of the Collatz graph

    Pages 31-75

    Wirsching, Günther J.

  • 3-adic averages of counting functions

    Pages 76-95

    Wirsching, Günther J.

  • An asymptotically homogeneous Markov chain

    Pages 96-122

    Wirsching, Günther J.

Buy this book

eBook 29,74 €
price for Spain (gross)
  • ISBN 978-3-540-69677-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 36,39 €
price for Spain (gross)
  • ISBN 978-3-540-63970-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
The Dynamical System Generated by the 3n+1 Function
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1681
Copyright
1998
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-69677-3
DOI
10.1007/BFb0095985
Softcover ISBN
978-3-540-63970-1
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VIII, 164
Topics