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arXiv · 2004.07357

Bounded Orbits of Quadratic Collatz-type Recursions

H. Sedaghat
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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).

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H. Sedaghat. 2020-04-15. Bounded Orbits of Quadratic Collatz-type Recursions. https://arxiv.org/abs/2004.07357

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