The Dynamical System Generated by the 3n+1 Function
Authors: Wirsching, Günther J.
Free PreviewBuy this book
- 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)
-
-
Introduction
Pages 1-9
-
Some ideas around 3n+1 iterations
Pages 10-30
-
Analysis of the Collatz graph
Pages 31-75
-
3-adic averages of counting functions
Pages 76-95
-
An asymptotically homogeneous Markov chain
Pages 96-122
-
Table of contents (6 chapters)
Recommended for you
Bibliographic Information
- Bibliographic Information
-
- Book Title
- The Dynamical System Generated by the 3n+1 Function
- Authors
-
- Günther J. Wirsching
- 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
