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Geometric two-scale convergence on manifold and applications to the Vlasov equation

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  • We develop and we explain the two-scale convergence in the covariant formalism, i.e. using differential forms on a Riemannian manifold. For that purpose, we consider two manifolds $M$ and $Y$, the first one contains the positions and the second one the oscillations. We establish some convergence results working on geodesics on a manifold. Then, we apply this framework on examples.
    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


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