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 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.