<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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 <italic>J<sub>α</sub></italic> conformed by points with the same pointwise dimension, and obtain the <italic>D</italic>(<italic>α</italic>) singularity spectrum.</p>
</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.

Boltzmann and the Statistical Multifractals

Universidad Autónoma Metropolitana-Iztapalapa

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Boltzmann and the Statistical Multifractals"}

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...

Boltzmann and the Statistical Multifractals

Article Category: Papers dedicated to the memory of Valetnin Afraymovich (1945-2018)

Published Online: May 12, 2019

Page range: 197 - 208

Received: Jan 19, 2019

Accepted: Mar 24, 2019

DOI: https://doi.org/10.2478/AMNS.2019.1.00007

Keywords
Boltzmann’s formulation, statistical multifractals, pointwise dimension, Hausdorff dimension

© 2019 Del Río-Correa J.L. et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Boltzmann and the Statistical Multifractals

Article Category: Papers dedicated to the memory of Valetnin Afraymovich (1945-2018)

Published Online: May 12, 2019

Page range: 197 - 208

Received: Jan 19, 2019

Accepted: Mar 24, 2019

DOI: https://doi.org/10.2478/AMNS.2019.1.00007

KeywordsBoltzmann’s formulation, statistical multifractals, pointwise dimension, Hausdorff dimension

© 2019 Del Río-Correa J.L. et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Boltzmann’s formulation, statistical multifractals, pointwise dimension, Hausdorff dimension