Abstract
We introduce a concept of relative rotation number to unify many different approaches of rotation number in non-linear dynamical systems. We present an ergodic result of existence a.s. for stochastic systems. In higher dimension, we show that the natural idea of projecting into a plane does work well a.s. for any plane (different from deterministic systems where projections may be degenerate). A number of further properties (invariance by homotopy and by conjugacy) and applications are presented.
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Acknowledgements
Research by Pedro J. Catuogno was partially supported by FAPESP, grant no. 02/10246-2. Research by Diego Sebastian Ledesma was supported by FAPESP, grant no. 04/13758-0. Research by Paulo R.C. Ruffino was partially supported by CNPq, grant no. 301112/2003-7 and FAPESP, grant no. 02/10246-2.