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Towards Multifractality through an Ernst-Type Potential in Complex Systems Dynamics.

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  • 1Department of Biophysics and Medical Physics, "Grigore T. Popa" University of Medicine and Pharmacy, 700115 Iasi, Romania.

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Summary
This summary is machine-generated.

Scale Relativity Theory and Space-Time Theory share SL(2R) invariance, enabling a unified description of complex systems. This allows non-differentiable dynamics to be functional within standard General Relativity and Quantum Mechanics.

Keywords:
Ernst potentialSL (2R) groupcomplex systemsmultifractalityscale relativity theoryspace–time theory

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Area of Science:

  • Theoretical Physics
  • Complex Systems Dynamics
  • Mathematical Physics

Background:

  • Scale Relativity Theory and Space-Time Theory (General Relativity) are fundamental frameworks.
  • Both theories describe complex systems but use different mathematical formalisms.
  • A common mathematical structure could unify their descriptions.

Purpose of the Study:

  • To establish correspondences between Scale Relativity Theory and Space-Time Theory.
  • To explore the implications of shared mathematical invariances for complex systems.
  • To enable a non-differentiable description of complex systems within standard physics.

Main Methods:

  • Identifying shared SL(2R)-type invariance in the multifractal Schrödinger equation and General Relativity equations.
  • Utilizing an Ernst-type potential from General Relativity.
  • Employing a multi-fractal tensor from Scale Relativity Theory.

Main Results:

  • Demonstrated that both theories exhibit the same SL(2R)-type invariance.
  • Highlighted the role of Ernst-type potentials and multi-fractal tensors in describing complex systems.
  • Established a functional framework for non-differentiable complex systems dynamics.

Conclusions:

  • Correspondences between Scale Relativity and General Relativity are possible.
  • Shared SL(2R) invariance provides a bridge between the theories.
  • Non-differentiable dynamics can be integrated into standard physics frameworks.