E-Book, Englisch, Band 1681, 164 Seiten, eBook
Reihe: Lecture Notes in Mathematics
Wirsching The Dynamical System Generated by the 3n+1 Function
1998
ISBN: 978-3-540-69677-3
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, Band 1681, 164 Seiten, eBook
Reihe: Lecture Notes in Mathematics
ISBN: 978-3-540-69677-3
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
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.
