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The Dynamical System Generated by the 3n+1 Function

Medium: Buch
ISBN: 978-3-540-63970-1
Verlag: Springer Berlin Heidelberg
Erscheinungstermin: 19.02.1998
Lieferfrist: bis zu 10 Tage

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.


Produkteigenschaften


  • Artikelnummer: 9783540639701
  • Medium: Buch
  • ISBN: 978-3-540-63970-1
  • Verlag: Springer Berlin Heidelberg
  • Erscheinungstermin: 19.02.1998
  • Sprache(n): Englisch
  • Auflage: 1998
  • Serie: Lecture Notes in Mathematics
  • Produktform: Kartoniert
  • Gewicht: 271 g
  • Seiten: 164
  • Format (B x H x T): 155 x 235 x 10 mm
  • Ausgabetyp: Kein, Unbekannt
Autoren/Hrsg.

Autoren

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.