TY  - BOOK
AU  - Wirsching,Günther J.
ED  - SpringerLink (Online service)
TI  - The Dynamical System Generated by the 3n+1 Function
T2  - Lecture Notes in Mathematics,
SN  - 9783540696773
AV  - QA241-247.5 
U1  - 512.7 23
PY  - 1998///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Information theory
KW  - Number theory
KW  - Number Theory
KW  - Theory of Computation
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/BFb0095985
ER  -