The dynamical system generated by the 3n + 1 function
By: Günther J. Wirsching.
Series: Lecture notes in mathematics,; 1681; Lecture notes in mathematics (Springer-Verlag) ;; 1681.
Publisher: Springer
Published: 1998
Place of publication: Berlin; New York
Language: eng
Number of pages: 158
Subjects: Sequences (Mathematics); Combinatorial probabilities; Convergence
Description: 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.
Notes: Includes bibliographical references (p. [141]-145) and indexes.