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Multiple Lie Derivatives and Forests

Abstract : We obtain a complete time expansion of the pull-back operator generated by a real analytic flow of real analytic automorphisms acting on analytic tensor sections of a manifold. Our expansion is given in terms of multiple Lie derivatives. Motivated by this expansion, we provide a rather simple and explicit estimate for higher order covariant derivatives of multiple Lie derivatives acting on smooth endomorphism sections of the tangent bundle of a manifold. We assume the covariant derivative to be torsion free. The estimate is given in terms of Dyck polynomials. The proof uses a new result on the combinatorics of rooted labeled ordered forests and Dyck polynomials.
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https://hal.archives-ouvertes.fr/hal-02349044
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Submitted on : Tuesday, November 5, 2019 - 3:13:00 PM
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  • HAL Id : hal-02349044, version 1

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Florent Hivert, Nefton Pali. Multiple Lie Derivatives and Forests. Advances in Mathematics, Elsevier, 2019. ⟨hal-02349044⟩

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