Günther J. Wirsching

The Dynamical System Generated by the 3n+1 Function

• Broschiertes Buch

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

• Lecture Notes in Mathematics 1681
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 10649733, 978-3-540-63970-1
• 1998
• Seitenzahl: 172
• Erscheinungstermin: 19. Februar 1998
• Englisch
• Abmessung: 235mm x 155mm x 10mm
• Gewicht: 298g
• ISBN-13: 9783540639701
• ISBN-10: 3540639705
• Artikelnr.: 09239953

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.