For a wide class of Collatz-type maps, the paper characterizes nonzero periodic points as integer values of a (p,q)-adic interpolation function and recasts the periodic-point question as a translate-density question, under hypotheses the Collatz map satisfies.
The p-adic ergodic theory and ap- plications
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$\left(p,q\right)$-adic Analysis and the Collatz Conjecture
For a wide class of Collatz-type maps, the paper characterizes nonzero periodic points as integer values of a (p,q)-adic interpolation function and recasts the periodic-point question as a translate-density question, under hypotheses the Collatz map satisfies.