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Local (sub) Finslerian geometry for the maximum norms in dimension 2 *

Abstract : We consider specific sub-Finslerian structures in the neighborhood of 0 in R 2 , defined by fixing a familly of vector fields (F1, F2) and considering the norm defined on the non constant rank distribution ∆ = vect{F1, F2} by |G| = inf u {max{|u1|, |u2|} | G = u1F1 + u2F2}. If F1 and F2 are not proportionnal at p then we obtain a Finslerian structure; if not, the structure is sub-Finslerian on a distribution with non constant rank. We are interested in the study of the local geometry of these Finslerian and sub-Finslerian structures: generic properties, normal form, short geodesics, cut locus, switching locus and small spheres.
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https://hal.archives-ouvertes.fr/hal-02004271
Contributor : Grégoire Charlot Connect in order to contact the contributor
Submitted on : Friday, February 1, 2019 - 4:21:51 PM
Last modification on : Tuesday, May 11, 2021 - 11:36:04 AM
Long-term archiving on: : Thursday, May 2, 2019 - 10:43:39 PM

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A.-L Ali, Grégoire Charlot. Local (sub) Finslerian geometry for the maximum norms in dimension 2 *. Journal of Dynamical and Control Systems, 2019. ⟨hal-02004271⟩

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