  The dynamics of Maxwell-dilaton theory in Minkowski spacetime are studied
using fully nonlinear, numerical evolutions. This model represents the
flat-space sector of Einstein-Maxwell-Dilaton theory which has attracted
interest recently because it is a well-posed alternative to general relativity,
and it also represents the abelian sector of Yang-Mills-Dilaton. As such,
understanding its dynamics may shed light on the dynamics of the respective
larger systems. In particular, we study electric, magnetic, and dyonic
monopoles as well as the flux tubes studied previously by Gibbons and Wells.
Some scenarios produce large gradients that an increasing adaptive mesh
refinement fails to resolve. This behavior is suggestive, although far from
conclusive, that the growth leads to singularity formation. No sharp transition
between singularity formation and either dispersion or stationarity is found,
unlike other nonlinear systems that have demonstrated behavior similar to black
hole critical behavior at such transitions.
