Differentiability and Fractality in Dynamics of Physical Systems by Ioan Merches

Differentiability and Fractality in Dynamics of Physical Systems

byIoan Merches, Maricel Agop

Kobo ebook | August 28, 2015

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Using Cartan's differential 1-forms theory, and assuming that the motion variables depend on Euclidean invariants, certain dynamics of the material point and systems of material points are developed. Within such a frame, the Newtonian force as mass inertial interaction at the intragalactic scale, and the Hubble-type repulsive interaction at intergalactic distances, are developed.

The wave-corpuscle duality implies movements on curves of constant informational energy, which implies both quantizations and dynamics of velocity limits.

Analysis of motion of a charged particle in a combined field which is electromagnetic and with constant magnetism implies fractal trajectories. Mechanics of material points in a fractalic space is constructed, and various applications — fractal atom, potential well, free particle, etc. — are discussed.


  • Principles of Motion in Invariantive Mechanics
  • Inertial Invariantive Motion of the Material Point
  • Field Invariantive Theories
  • Ondulatory Invariantive Theories. Wave-Corpuscule Duality
  • Invariantive Mechanics of Systems of Material Points
  • The Photon in Invariantive Ondulatory Theories
  • Lagrangian Approach in Invariantive Mechanics
  • Considerations on Invariantive Mechanics
  • Invariantive Mechanics of Rigid Body
  • Covariant Formulation of Conservation Laws in Invariantive Mechanics
  • Invariantive Mechanics and Informational Energy
  • Chaos Via Fractality in Gravitational Dynamical Systems
  • Fractality at Small Scale. Fractal Model of the Atom
  • Extended Fractal Hydrodynamic Model with an Arbitrary Fractal Dimension and Its Implications
  • Theory of Fractional Scale Relativity and Some Applications

Readership: Master, PhD students and professional researchers in the field of physics.
Key Features:

  • Theory of 1-forms is applied to dynamics of material points systems
  • Non-differentiability as a possible property of complex systems
  • The role played by informational energy in the definition of the constants of motion is discussed
Title:Differentiability and Fractality in Dynamics of Physical SystemsFormat:Kobo ebookPublished:August 28, 2015Publisher:World Scientific Publishing CompanyLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9814678406

ISBN - 13:9789814678407