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＜電子ブック＞
The Dynamical System Generated by the 3n+1 Function / by Günther J. Wirsching
(Lecture Notes in Mathematics. ISSN:16179692 ; 1681)

版	1st ed. 1998.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1998
本文言語	英語
大きさ	VIII, 164 p : online resource
著者標目	*Wirsching, Günther J author SpringerLink (Online service)
件　名	LCSH:Number theory LCSH:Computer science FREE:Number Theory FREE:Theory of Computation
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/BFb0095985

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