The limited Rademacher functions and Bernoulli convolutions associated with Pisot numbers
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The author gives a systematical study of the local structure and fractal dimensions of the limited Rademacher functions and Bernoulli convolutions associated with the Pisot numbers. These fractal dimensions can be expressed as some limits in terms of products of non-negative matrices. When a Pisot number is simple, the author obtains the precise formulas of the fractal dimensions and the multifractal formalism.
- Tsinghua University China (People's Republic of)
\(L^q\)-spectrum, Lq-spectrum, Mathematics(all), Metric theory of other algorithms and expansions; measure and Hausdorff dimension, multifractals, Hausdorff dimension, Multifractals, Pisot numbers, product of matrices, Information dimension, information dimension, Product of matrices, PV-numbers and generalizations; other special algebraic numbers; Mahler measure, Fractals, Hausdorff and packing measures, Real-valued functions in general topology, Limited Rademacher functions, limited Rademacher functions, Relations of ergodic theory with number theory and harmonic analysis, Entropy and other invariants, Bernoulli convolutions
\(L^q\)-spectrum, Lq-spectrum, Mathematics(all), Metric theory of other algorithms and expansions; measure and Hausdorff dimension, multifractals, Hausdorff dimension, Multifractals, Pisot numbers, product of matrices, Information dimension, information dimension, Product of matrices, PV-numbers and generalizations; other special algebraic numbers; Mahler measure, Fractals, Hausdorff and packing measures, Real-valued functions in general topology, Limited Rademacher functions, limited Rademacher functions, Relations of ergodic theory with number theory and harmonic analysis, Entropy and other invariants, Bernoulli convolutions
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