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arXiv · 1806.08306

Multiple Lie Derivatives and Forests

Florent Hivert·Nefton Pali
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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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Florent Hivert, Nefton Pali. 2018-06-21. Multiple Lie Derivatives and Forests. https://arxiv.org/abs/1806.08306

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