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The Juggler map sends an even positive integer to the integer part of its square root and an odd positive integer to the integer part of its three-halves power. We obtain restrictions on hypothetical nontrivial cycles. For a cycle with minimum n, length L, and o odd steps, we prove the cycle-financing inequality nlog n...
The Juggler map sends an even positive integer to the integer part of its square root and an odd positive integer to the integer part of its three-halves power. We prove that every nonempty set A closed under taking preimages satisfies ∑_(n ∈ A, n ≤ x)1/n ≥ c(log x)^(λ), for all sufficiently large x and every 0 < λ < λ...
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