Kepler sets of linear recurrence sequences

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2025年2月8日

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D. Berend,
R. Kumar

摘要

The Kepler set of a sequence $(a_n)_{n=0}^\infty$ ${(a_{n})}_{n = 0}^{\infty}$ is the closure of the set of consecutive ratios $\{a_{n+1}/a_{n} : n\geq 0\}$ ${a_{n + 1} / a_{n} : n \geq 0}$ . Following several studies, dealing with Kepler sets of recurrence sequences of order 2, we study here the case of recurrences of any order.