Scale dynamical origin of modification or addition of potential in   mechanics. A possible framework for the MOND theory and the dark matter
  Using our mathematical framework developed in \cite{cresson-pierret_scale} called \emph{scale dynamics}, we propose in this paper a new way of interpreting the problem of adding or modifying potentials in mechanics and specifically in galactic dynamics. An application is done for the two-body problem with a Keplerian potential showing that the velocity of the orbiting body is constant. This would explain the observed phenomenon in the flat rotation curves of galaxies without adding \emph{dark matter} or modifying Newton's law of dynamics. 
Fr\'ed\'eric Pierret
math-ph astro-ph.EP astro-ph.GA math.DS math.MP