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- W1618159404 abstract "Let $F(z)=z-H(z)$ with $o(H(z))geq 2$ be a formal map from $bC^n$ to $bC^n$ and $G(z)$ the formal inverse of $F(z)$. In this paper, we fist study the deformation $F_t(z)=z-tH(z)$ and its formal inverse map $G_t(z)$. We then derive two recurrent formulas for the formal inverse $G(z)$. The first formula in certain situations provides a more efficient method for the calculation of $G(z)$ than other well known inversion formulas. The second one is differential free but only works when $H(z)$ is homogeneous of degree $dgeq 2$. Finally, we reveal a close relationship of the inversion problem with a Cauchy problem of a PDE. When the Jacobian matrix $JF(z)$ is symmetric, the PDE coincides with the $n$-dimensional inviscid Burgers' equation in Diffusion theory." @default.
- W1618159404 created "2016-06-24" @default.
- W1618159404 creator A5070925864 @default.
- W1618159404 date "2003-05-12" @default.
- W1618159404 modified "2023-09-27" @default.
- W1618159404 title "Recurrent Inversion Formulas" @default.
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