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Area of Science:

  • Physics
  • Mathematics
  • Information Theory

Background:

  • Newtonian mechanics describes motion based on forces and trajectories.
  • Multifractal dynamics offer a complex framework for analyzing irregular systems.
  • Information theory principles can influence physical system behaviors.

Purpose of the Study:

  • To explore the connection between multifractal dynamics and Newtonian behaviors.
  • To analyze the geometric properties of multifractal motion.
  • To link multifractal dynamics to general relativity.

Main Methods:

  • Analysis of motion geodesics within a multifractal paradigm.
  • Application of the Cayley-Klein metric principle to eccentricity geometry.
  • Harmonic mappings between Euclidean space and the Lobachevsky plane (Poincaré metric).

Main Results:

  • Shannon's information functionality induces multifractal-type Newtonian behaviors.
  • The center of force and trajectory differ in multifractal motion, measured by eccentricity.
  • Eccentricity geometry maps to Lobachevsky plane geometry.
  • Ernst potential in general relativity gains a classical interpretation.
  • Multifractal dynamics manifest as local gravitational fields.

Conclusions:

  • Multifractal dynamics provide a framework for understanding Newtonian-like behaviors and their relation to gravity.
  • Geometric principles, including Lobachevsky geometry, are crucial for describing these complex dynamics.
  • This paradigm unifies aspects of classical mechanics, information theory, and general relativity.