# Rotation numbers of perturbations of smooth dynamics

@article{Gourmelon2020RotationNO, title={Rotation numbers of perturbations of smooth dynamics}, author={Nicolas Gourmelon}, journal={arXiv: Dynamical Systems}, year={2020} }

The small perturbations of a linear cocycle have a relative rotation number associated to each pair formed of an invariant measure of the base dynamics and a $2$-dimensional bundle of the finest dominated splitting (provided that some orientation is preserved). The properties of that relative rotation number allow some small steps towards dichotomies between complex eigenvalues and dominated splittings in higher dimensions and higher regularity.

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