کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8905038 1633763 2018 79 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Projections of planar Mandelbrot random measures
ترجمه فارسی عنوان
پیش بینی های اندازه گیری تصادفی ماندلبرت مسطح
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
چکیده انگلیسی
Let μ be a planar Mandelbrot measure and π⁎μ its orthogonal projection on one of the principal axes. We study the thermodynamic and geometric properties of π⁎μ. We first show that π⁎μ is exact dimensional, with dim⁡(π⁎μ)=min⁡(dim⁡(μ),dim⁡(ν)), where ν is the Bernoulli product measure obtained as the expectation of π⁎μ. We also prove that π⁎μ is absolutely continuous with respect to ν if and only if dim⁡(μ)>dim⁡(ν). Our results provides a new proof of Dekking-Grimmett-Falconer formula for the Hausdorff and box dimension of the topological support of π⁎μ, as well as a new variational interpretation. We obtain the free energy function τπ⁎μ of π⁎μ on a wide subinterval [0,qc) of R+. For q∈[0,1], it is given by a variational formula which sometimes yields phase transitions of order larger than 1. For q>1, it is given by min⁡(τν,τμ), which can exhibit first order phase transitions. This is in contrast with the analyticity of τμ over [0,qc). Also, we prove the validity of the multifractal formalism for π⁎μ at each α∈(τπ⁎μ′(qc−),τπ⁎μ′(0+)].
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 325, 5 February 2018, Pages 640-718
نویسندگان
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