English

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).

Keywords

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

R2 v1 2026-06-23T14:53:00.004Z