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

<p>A new formulation of the informational entropy on multifractal manifolds is proposed. In such a context, some connections with known results from the dynamics of complex systems are presented: correlations of SL(2ℝ) groups with Hamiltonian formalism, simultaneous invariances between two groups (coordinate group and parametric group), linear harmonic oscillator/oscillator ensemble dynamics from the perspective of SL(2ℝ) groups, uncertainty relations on multifractal manifolds etc. Moreover, the existence of a multifractal perspective in the complex dynamics analysis allows direct correspondences with deep learning algorithms.</p>
</abstract>

A new formulation of the informational entropy on multifractal manifolds is proposed. In such a context, some connections with known results from the dynamics of complex systems are presented: correlations of SL(2ℝ) groups with Hamiltonian formalism, simultaneous invariances between two groups (coordinate group and parametric group), linear harmonic oscillator/oscillator ensemble dynamics from the perspective of SL(2ℝ) groups, uncertainty relations on multifractal manifolds etc. Moreover, the existence of a multifractal perspective in the complex dynamics analysis allows direct correspondences with deep learning algorithms.

Some Implications of the Multifractal Informational Entropy

“Alexandru Ioan Cuza” University of Iași

“Gheorghe Asachi” Technical University of Iași

Department of Concrete Structures, Building Materials, Technology and Management

BULETINUL INSTITUTULUI POLITEHNIC DIN IAȘI. Secția Matematica. Mecanică Teoretică. Fizică

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

{"article-title":"Some Implications of the Multifractal Informational Entropy"}

A new formulation of the informational entropy on multifractal manifolds is proposed. In such a context, some connections with known results from the dynamics...

Some Implications of the Multifractal Informational Entropy

Pubblicato online: 10 apr 2023

Pagine: 7 - 22

Ricevuto: 11 ago 2022

Accettato: 18 set 2022

DOI: https://doi.org/10.2478/bipmf-2022-0011

Parole chiave
SL(2ℝ) group, Hamiltonian formalism, harmonic oscillator, uncertainty relation, multifractal manifolds

© 2022 Gabriel Gavriluț et al., published by Sciendo

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

Some Implications of the Multifractal Informational Entropy

Pubblicato online: 10 apr 2023

Pagine: 7 - 22

Ricevuto: 11 ago 2022

Accettato: 18 set 2022

DOI: https://doi.org/10.2478/bipmf-2022-0011

Parole chiaveSL(2ℝ) group, Hamiltonian formalism, harmonic oscillator, uncertainty relation, multifractal manifolds

© 2022 Gabriel Gavriluț et al., published by Sciendo

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

Parole chiave
SL(2ℝ) group, Hamiltonian formalism, harmonic oscillator, uncertainty relation, multifractal manifolds