Author | Wirsching, Gรผnther J. author |
---|---|

Title | The Dynamical System Generated by the 3n+1 Function [electronic resource] / by Gรผnther J. Wirsching |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1998 |

Connect to | http://dx.doi.org/10.1007/BFb0095985 |

Descript | VIII, 164 p. online resource |

SUMMARY

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

CONTENT

Some ideas around 3n+1 iterations -- Analysis of the Collatz graph -- 3-adic averages of counting functions -- An asymptotically homogeneous Markov chain -- Mixing and predecessor density

Mathematics
Computers
Number theory
Mathematics
Number Theory
Theory of Computation