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[null,"1.","Record Nr.",null,"UNISA996466864403316"]
[null,null,"Autore",null,"Wirsching Günther J. <1960->"]
[null,null,"Titolo",null,"The dynamical system generated by the 3n + 1 function / / Günther J Wirsching"]
[null,null,"Pubbl/distr/stampa",null,"Berlin : , : Springer-Verlag, , [1998]"]
[{"$nulls":4},"©1998"]
[null,null,"ISBN",null,"3-540-69677-6"]
[null,null,"Edizione",null,"[1st ed. 1998.]"]
[null,null,"Descrizione fisica",null,"1 online resource (VIII, 164 p.)"]
[null,null,"Collana",null,"Lecture notes in mathematics ; ; 1681"]
[null,null,"Disciplina",null,"519.2"]
[null,null,"Soggetti",null,"Combinatorial probabilities"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Bibliographic Level Mode of Issuance: Monograph"]
[null,null,"Nota di contenuto",null,"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."]
[null,null,null,"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."]