The Dynamical System Generated by the 3n+1 Function

1. Auflage 1998
ISBN: 978-3-540-63970-1
Verlag: Springer

Buch, Englisch, 164 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 271 g

Reihe: Lecture Notes in Mathematics

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.

Wirsching, Günther J.

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Logik, formale Sprachen, Automaten
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

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.