Abstract
The least action principle is established for the dynamics of a test particle in a dilaton-Maxwell background. These dynamics and background are invariant under the action of the dilatation transformation; explicit form of the corresponding generalization of the Lorentz force is established for the considered model. On a stationary background, we have found the integral of motion of the energy type. This integral is used to resolve the radial dynamics of test particles in a spherically symmetric electrostatic background.
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