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Misiurewicz Maps are Rare

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Abstract:

In any real-analytic family of S-unimodal maps with non-constant combinatorics, the set of parameters corresponding to maps with Misiurewicz (non-recurrent) dynamics has Lebesgue measure zero. In particular, this is the case for the logistic family, answering an old question.

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Authors and Affiliations

  1. Department of Mathematics, State University of New York at Stony Brook, Stony Brook, NY 11794-3651, USA. E-mail: duncan@math.sunysb.edu, , , , , , US

    Duncan Sands

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  1. Duncan Sands
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Received: 8 September 1997 / Accepted: 13 February 1998

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Sands, D. Misiurewicz Maps are Rare . Comm Math Phys 197, 109–129 (1998). https://doi.org/10.1007/s002200050444

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  • DOI: https://doi.org/10.1007/s002200050444

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