Abstract
Following the ideas of Arnold and Seigal–Yakovenko, we prove that the space of matrix coefficients of a formal Lie group action belongs to a Noetherian ring. Using this result, we extend the uniform intersection multiplicity estimates of these authors from the abelian case to general Lie groups. We also demonstrate a simple new proof for a jet-determination result of Baouendi et al.
In the second part of the paper we use similar ideas to prove a result on embedding formal diffeomorphisms in one-parameter groups extending a result of Takens. In particular, this implies that the results of Arnold and Seigal–Yakovenko are formal consequences of our result for Lie groups.
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The author was supported by the Banting Postdoctoral Fellowship and the Rothschild Fellowship.
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BINYAMINI, G. FINITENESS PROPERTIES OF FORMAL LIE GROUP ACTIONS. Transformation Groups 20, 939–952 (2015). https://doi.org/10.1007/s00031-015-9333-x
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DOI: https://doi.org/10.1007/s00031-015-9333-x