# The Dynamical System Generated by the 3n+1 Function

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

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

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.

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

- 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
- About this book