Bounded Orbits of Quadratic Collatz-type Recursions
Dynamical Systems
2020-04-17 v1 Number Theory
Abstract
We characterize all bounded orbits of two similar Collatz-type quadratic mappings of the set of non-negative integers. In one case, where cycles of all possible lengths may occur, an orbit is bounded if and only if it reaches a cycle. For the other map we prove that every bounded orbit must reach 0 (in particular, there are no cycles).
Cite
@article{arxiv.2004.07357,
title = {Bounded Orbits of Quadratic Collatz-type Recursions},
author = {H. Sedaghat},
journal= {arXiv preprint arXiv:2004.07357},
year = {2020}
}
Comments
Eight pages