LEADER 02544nam 2200589 450 001 996466864403316 005 20220303141156.0 010 $a3-540-69677-6 024 7 $a10.1007/BFb0095985 035 $a(CKB)1000000000437332 035 $a(SSID)ssj0000322751 035 $a(PQKBManifestationID)12099110 035 $a(PQKBTitleCode)TC0000322751 035 $a(PQKBWorkID)10289903 035 $a(PQKB)10004845 035 $a(DE-He213)978-3-540-69677-3 035 $a(MiAaPQ)EBC5595389 035 $a(Au-PeEL)EBL5595389 035 $a(OCoLC)1076258602 035 $a(MiAaPQ)EBC6842781 035 $a(Au-PeEL)EBL6842781 035 $a(OCoLC)1113609871 035 $a(PPN)15521764X 035 $a(EXLCZ)991000000000437332 100 $a20220303d1998 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 14$aThe dynamical system generated by the 3n + 1 function /$fGu?nther J Wirsching 205 $a1st ed. 1998. 210 1$aBerlin :$cSpringer-Verlag,$d[1998] 210 4$dİ1998 215 $a1 online resource (VIII, 164 p.) 225 1 $aLecture notes in mathematics ;$v1681 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-63970-5 327 $aSome 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. 330 $aThe 3n+1 function T is defined by T(n)=n/2 for n even, and T(n)=(3n+1)/2 for n odd. The famous 3n+1 conjecture, which remains open, states that, for any starting number n>0, iterated application of T to n eventually produces 1. After a survey of theorems concerning the 3n+1 problem, the main focus of the book are 3n+1 predecessor sets. These are analyzed using, e.g., elementary number theory, combinatorics, asymptotic analysis, and abstract measure theory. The book is written for any mathematician interested in the 3n+1 problem, and in the wealth of mathematical ideas employed to attack it. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1681. 606 $aCombinatorial probabilities 615 0$aCombinatorial probabilities. 676 $a519.2 700 $aWirsching$b Gu?nther J.$f1960-$0351066 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466864403316 996 $aThe dynamical system generated by the 3n + 1 function$92787162 997 $aUNISA