Günther J. Wirsching

The Dynamical System Generated by the 3n+1 Function (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 164
• Erscheinungstermin: 14. November 2006
• Englisch
• ISBN-13: 9783540696773
• Artikelnr.: 53134925

Inhaltsangabe

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.