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Towards Stochasticity through Joint Invariant Functions of Two Isomorphic Lie Algebras of SL(2R) Type

by Maricel Agop 1,† and Mitică Craus 2,*,†
1
Department of Physics, Gheorghe Asachi Technical University, Iaşi 700050, Romania
2
Department of Computers, Gheorghe Asachi Technical Univeristy, Iaşi 700050, Romania
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2020, 12(2), 226; https://doi.org/10.3390/sym12020226
Received: 24 November 2019 / Revised: 3 January 2020 / Accepted: 15 January 2020 / Published: 3 February 2020
In the motion fractal theory, the scale relativity dynamics of any complex system are described through various Schrödinger or hydrodynamic type fractal “regimes”. In the one dimensional stationary case of Schrödinger type fractal “regimes”, synchronizations of complex system entities implies a joint invariant function with the simultaneous action of two isomorphic groups of the S L ( 2 R ) type as solutions of Stoka type equations. Among these joint invariant functions, Gaussians become in the Jeans’s sense, probability density (i.e., stochasticity) whenever the information on the complex system analyzed is fragmentary. In the two-dimensional case of hydrodynamic type fractal “regimes” at a non-differentiable scale, the soliton and soliton-kink of fractal type of the velocity field generate the minimal vortex of fractal type that becomes the source of all turbulences in the complex systems dynamics. Some correlations of our model to experimental data were also achieved. View Full-Text
Keywords: Lie groups; transformations; invariance; normalized Gaussian; stochasticity; uncertainty relation; fractal Lie groups; transformations; invariance; normalized Gaussian; stochasticity; uncertainty relation; fractal
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Agop, M.; Craus, M. Towards Stochasticity through Joint Invariant Functions of Two Isomorphic Lie Algebras of SL(2R) Type. Symmetry 2020, 12, 226.

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