The Dynamical System Generated by the 3n+1 Function

• Κύριος συγγραφέας: Wirsching, Günther J. (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1998.
• Έκδοση: 1st ed. 1998.
• Σειρά: Lecture Notes in Mathematics, 1681
• Θέματα: Number theory.; Computers.; Number Theory.; Theory of Computation.

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 focu...

Πίνακας περιεχομένων:

• 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.