The Dynamical System Generated by the 3n+1 Function / / by Günther J. Wirsching

• Autore: Wirsching Günther J. <1960->
• Pubblicazione: Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1998
• Edizione: 1st ed. 1998.
• Descrizione fisica: 1 online resource (VIII, 164 p.)
• Disciplina: 519.2
• Soggetto topico: Number theory; Computer science; Number Theory; Theory of Computation
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di contenuto: 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.
• Sommario/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.
• Titolo autorizzato: The Dynamical System Generated by the 3n+1 Function
• ISBN: 3-540-69677-6
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910146298303321
• Lo trovi qui: Univ. Federico II
• Serie: Lecture Notes in Mathematics, . 1617-9692 ; ; 1681