Smoothness of the Lq‐Spectrum of Self‐Similar Measures with Overlaps

By De-Jun Feng. 2003

56 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1c712b685cf32d4dc5b35669f65c9c4dec616536

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

1. Huyi Hu
2. Ka-Sing Lau
3. Eric Olivier
4. De-Jun Feng
5. Wen Huang

In Mathematical Physics

1. De-Jun Feng
2. Wen Huang
3. Ka-Sing Lau
4. Huyi Hu
5. Eric Olivier
6. Yongluo Cao
7. A. Kaenmaki
8. Xiangdong Ye

In Statistical and Nonlinear Physics

1. De-Jun Feng
2. Wen Huang
3. Huyi Hu
4. Ka-Sing Lau
5. Eric Olivier
6. Yongluo Cao
7. A. Kaenmaki
8. Daniel Thompson

Citations in the corpus

• Dimension theory of iterated function systems (2009, methodology): “, [16, 17, 35, 37, 39]), and furthermore the Hausdorff dimension of K can be computed (see, e.”
• The limited Rademacher functions and Bernoulli convolutions associated with Pisot numbers (2005, methodology): “dynamical system. For all the Pisot reciprocals besides simple Pisot reciprocals, by extending an idea in this paper and using a result on the product of non-negative matrices in [15], Feng [ 14 ] recently proved that (q) is always differentiable for q> 0 and (1.4) holds for q> 0.”
• The thermodynamic formalism for sub-additive potentials (2007, background): “1 are closely related to the dimension estimates for a broad class of Cantor-like sets and dynamical repellers [1, 11], the multifractal structure of iterated function systems with overlaps [12, 20], the distribution of Lyapunov exponents of a dynamical system [9, 13].”
• Multifractal analysis of weak Gibbs measures and phase transition—application to some Bernoulli convolutions (2003, background): “[ 14 ]), the general case of a Pisot number seems to remain a difficult problem.”
• Lyapunov exponents for products of matrices and multifractal analysis. Part II: General matrices (2003, background): “Combining the results in [16] and [30], under the finite type condition, we have dimH Eμ(α) = inf{αq−τ(q) : q ∈ R} for all those α ∈ {τ ′(t) : t > 0}.”
• Multifractal formalism for self-similar measures with weak separation condition (2009, background): “It was shown in [ 9 ] that for a self-similar measure on its generating IFS is equi-contractive and satises the nite type condition, then the Lq-spectrum is always dierentiable over (0 ;1), furthermore, an analogue of Theorem 1.2 holds [11].”