The Dynamical System Generated by the 3n+1 Function: 1681 - Brossura

Wirsching, Günther J.

Brossura

ISBN 10: 3540639705 ISBN 13: 9783540639701

Casa editrice: Springer, 2009

Riassunto

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.

Su questo libro

Contenuti

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.

Product Description

Book by Wirsching Gnther J

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2009
• Lingua: Inglese
• ISBN 10: 3540639705
• ISBN 13: 9783540639701
• Rilegatura: Copertina flessibile
• Numero di pagine: 172
• Contatto del produttore: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Germania