The dynamical system generated by the 3n + 1 function / / Günther J Wirsching

• Record Nr.: UNISA996466864403316
• Autore: Wirsching Günther J. <1960->
• Pubbl/distr/stampa: Berlin : , : Springer-Verlag, , [1998]; ©1998
• ISBN: 3-540-69677-6
• Edizione: [1st ed. 1998.]
• Descrizione fisica: 1 online resource (VIII, 164 p.)
• Collana: Lecture notes in mathematics ; ; 1681
• Disciplina: 519.2
• Soggetti: Combinatorial probabilities
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• 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.