1. A Collatz-type conjecture on the set of rational numbers
- Author
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Javaheri, Mohammad
- Subjects
- *
RATIONAL numbers , *HYPOTHESIS , *SET theory , *NONNEGATIVE matrices , *NUMBER theory , *SEMIGROUPS (Algebra) - Abstract
Abstract: Let if , and if . We conjecture that the θ-orbit of every nonnegative rational number ends in 0. A weaker conjecture asserts that there are no positive rational fixed points for any map in the semigroup Λ generated by the maps and . In this paper, we prove that the asymptotic density of the set of maps in Λ that have rational fixed points is zero. Moreover, we prove that certain types of elements in the semigroup Λ cannot have rational fixed points. [Copyright &y& Elsevier]
- Published
- 2012
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