Manuel Inselmann

collaborators

3 papers

math.DS2024

An approximation of the Collatz map and a lower bound for the average total stopping time

Manuel Inselmann

Define the map $T$ on the positive integers by $T (m) = \frac{m}{2}$ if $m$ is even and by $T (m) = \frac{3 m + 1}{2}$ if $m$ is odd. Results of Terras and Everet…

math.DS2024

Almost all orbits of an analogue of the Collatz map on the reals attain bounded values

Manuel Inselmann

Motivated by a balanced ternary representation of the Collatz map we define the map $C_{R}$ on the positive real numbers by setting $C_{R} (x) = \frac{1}{2} x$ if $[x]$ i…

math.DS2024

On the average stopping time of the Collatz map in $F_{2} [x]$

Manuel Inselmann

Define the map $T_{1}$ on $F_{2} [x]$ by $T_{1} (f) = \frac{f}{x}$ if $f (0) = 0$ and $T_{1} (f) = \frac{( x + 1 ) f + 1}{x}$ if $f (0) = 1$ . For a non-zero polynomial $f$ let $τ_{1} (f)$ denote the lea…

An approximation of the Collatz map and a lower bound for the average total stopping time

Almost all orbits of an analogue of the Collatz map on the reals attain bounded values

On the average stopping time of the Collatz map in F2​[x]

On the average stopping time of the Collatz map in $F_{2} [x]$