The Dynamical System Generated by the 3n+1 Function
(Sprache: Englisch)
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...
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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.
Inhaltsverzeichnis zu „The Dynamical System Generated by the 3n+1 Function “
- Introduction- Analysis of the Collatz Graph
3-adic Averages of Counting Functions
- An Asymptotically Homogeneous Markov Chain
- Mixing and Predecessor Density
- Symbols
- Bibliography
- Index of Authors
- Index
Bibliographische Angaben
- Autor: Günther J. Wirsching
- 1998, 1998., 164 Seiten, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer
- ISBN-10: 3540639705
- ISBN-13: 9783540639701
- Erscheinungsdatum: 19.02.1998
Sprache:
Englisch
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