02743nam 22006495 450 991014629830332120250731082225.03-540-69677-610.1007/BFb0095985(CKB)1000000000437332(SSID)ssj0000322751(PQKBManifestationID)12099110(PQKBTitleCode)TC0000322751(PQKBWorkID)10289903(PQKB)10004845(DE-He213)978-3-540-69677-3(MiAaPQ)EBC5595389(Au-PeEL)EBL5595389(OCoLC)1076258602(MiAaPQ)EBC6842781(Au-PeEL)EBL6842781(OCoLC)1113609871(PPN)15521764X(EXLCZ)99100000000043733220121227d1998 u| 0engurnn|008mamaatxtccrThe Dynamical System Generated by the 3n+1 Function /by Günther J. Wirsching1st ed. 1998.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,1998.1 online resource (VIII, 164 p.) Lecture Notes in Mathematics,1617-9692 ;1681Bibliographic Level Mode of Issuance: Monograph3-540-63970-5 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.Lecture Notes in Mathematics,1617-9692 ;1681Number theoryComputer scienceNumber TheoryTheory of ComputationNumber theory.Computer science.Number Theory.Theory of Computation.519.2Wirsching Günther J.1960-351066MiAaPQMiAaPQMiAaPQBOOK9910146298303321The Dynamical System Generated by the 3n+1 Function4412835UNINA