Kepler sets of linear recurrence sequences

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