The Dynamical System Generated by the 3n+1 Function

Günther J. Wirsching (Autor)

Buch | Softcover

VIII, 164 Seiten

1998
Springer Berlin (Verlag)
978-3-540-63970-1 (ISBN)

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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.

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.

Erscheint lt. Verlag	19.2.1998
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	VIII, 164 p.
Verlagsort	Berlin
Sprache	englisch
Maße	216 x 279 mm
Gewicht	255 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	3n+1 problem • asymptotic analysis • Calculus • collatz graph • dynamical systems on N • Dynamisches System • Dynamische Systeme • Number Theory • p-adic distribution
ISBN-10	3-540-63970-5 / 3540639705
ISBN-13	978-3-540-63970-1 / 9783540639701
Zustand	Neuware