The multifractal spectra of certain planar recurrence sets in the continued fraction dynamical system

摘要

In this paper, we will introduce and study the planar recurrence level set <br>S(alpha, beta) := {(x, y) is an element of [0, 1)(2): (R) under bar(x, y) = alpha, (R) over bar (x, y) = beta}, 0 <= alpha <= beta <= infinity, <br>where (R) under bar(x, y) and (R) over bar (x, y) are the lower and upper quantitative hitting time indicators of y by x respectively in the continued fraction dynamical system. It is shown that the multifractal spectrum is always degenerate in a sense that it is constant independent of the choice of the level set.

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