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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.
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Details
1 Faculty of Physics, “Alexandru Ioan Cuza” University of Iași, Romania
2 Department of Agroeconomy, Iași University of Life Sciences, Romania
3 Department of Physics, “Gheorghe Asachi” Technical University of Iași, Romania
4 Department of Concrete Structures, Building Materials, Technology and Management, “Gheorghe Asachi” Technical University of Iași, Romania
5 Departament of Mathematics, University of Colorado, Boulder, USA