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Good’s Theorem for regular continued fraction states that the set of real numbers [Formula: see text] such that [Formula: see text] has Hausdorff dimension [Formula: see text]. We show an analogous result for the complex plane and Hurwitz Continued Fractions: the set of complex numbers whose Hurwitz Continued fraction [Formula: see text] satisfies [Formula: see text] has Hausdorff dimension 1, half of the ambient space’s dimension.

Abstract. On 10 May 2018, an active seismic crisis began on French island of Mayotte, which a year later will be shown to be related to offshore volcanic activity. It affects a vulnerable territory exposed to risks of many kinds (poverty, violence, lack of basic resources). In the absence of known events in human memory, the population is naive with regard to seismic and volcanic hazards. The concern is therefore very strong. In spite of a large number of publications, the communication set up by the main actors of the risk chain does not answer the population's concern. To understand why, we analyse a large corpus of the textual communications (press releases, web pages, scientific bulletins, reports, etc.) issued by the authorities and scientists from May 2018 to April 2021. We draw lessons on the communication strategy put in place in the first three years of the crisis; and we issue recommendations for improvement in the future, in Mayotte, but also elsewhere in contexts where comparable geo-crises may happen. We notably stress the importance of ensuring that communication is not overly technical, that it aims to inform rather than reassure, that it focuses on risk and not only on hazard and that it provides clues to possible risk scenarios.

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