Invariant densities for dynamical systems with random switching

@article{Bakhtin2012InvariantDF,
  title={Invariant densities for dynamical systems with random switching},
  author={Yuri Bakhtin and T. Hurth},
  journal={Nonlinearity},
  year={2012},
  volume={25},
  pages={2937-2952}
}
We consider a nonautonomous ordinary differential equation on a smooth manifold, with right-hand side that randomly switches between the elements of a finite family of smooth vector fields. For the resulting random dynamical system, we show that Hormander type hypoellipticity conditions are sufficient for uniqueness and absolute continuity of an invariant measure. 
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