Boltzmann and the Statistical Multifractals-Reference-Cited by-同舟云学术

Boltzmann and the Statistical Multifractals

Published:2019-01-01 Issue:1 Volume:4 Page:197-208
ISSN:2444-8656
Container-title:Applied Mathematics and Nonlinear Sciences
language:en
Short-container-title:

Author:

Río-Correa J.L. Del¹,J. López-García²,G. Durán-Meza¹

Affiliation:

1. Universidad Autónoma Metropolitana-Iztapalapa , Departamento de Física , Física , México

2. UNAM - FES Acatlán , División de Matemáticas e Ingeniería , Ingeniería , México

Abstract

Abstract We extend the Boltzmann’s ideas that describe the evolution to the equilibrium of many body systems to the multifractal decomposition of the unitary interval 𝕀, in terms of sets Jα conformed by points with the same pointwise dimension, and obtain the D(α) singularity spectrum.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Engineering (miscellaneous),Modeling and Simulation,General Computer Science

Link

https://www.sciendo.com/pdf/10.2478/AMNS.2019.1.00007

Reference14 articles.

1. T.C. Halsey, M.H. Jensen, L.P. Kadanoff, I. Procaccia, and B. I. Shraimar (1986). Fractal measures and their singularities: The characterization of strange sets. Phys. Rev. A 33, 1141-1151.

2. Ludwig Boltzmann (1964). Lectures in gas theory. Dover Publications.

3. Radu Balescu (1975). Equilibrium and nonequilibrium statistical mechanics. John Wiley and Sons.

4. H.G. Eggleston (1949). The fractional dimension of a set defined by the decimal properties. Quart.J.Math., Oxford Ser.20, 31-36.

5. Yakov Pesin and Vaughn Climenhaga (2009). Lectures on fractal geometry and dynamical systems, American Mathematical Society. A discussion on the pointwise dimension is found in Lecture 16 page 123.

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