Office of Academic Resources
Chulalongkorn University
Chulalongkorn University

Home / Help

AuthorWirsching, Gรผnther J. author
TitleThe Dynamical System Generated by the 3n+1 Function [electronic resource] / by Gรผnther J. Wirsching
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1998
Connect tohttp://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



Location



Office of Academic Resources, Chulalongkorn University, Phayathai Rd. Pathumwan Bangkok 10330 Thailand

Contact Us

Tel. 0-2218-2929,
0-2218-2927 (Library Service)
0-2218-2903 (Administrative Division)
Fax. 0-2215-3617, 0-2218-2907

Social Network

  line

facebook   instragram