Differentiability And Fractality In Dynamics Of Physical Systems

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

• 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