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Recurrent Inversion Formulas | | Wenhua Zhao
; | | Date: |
12 May 2003 | | Subject: | Complex Variables; Algebraic Geometry MSC-class: 32H02, 14R15 | math.CV math-ph math.AG math.MP | | Abstract: | Let $F(z)=z-H(z)$ with $o(H(z))geq 2$ be a formal map from $C^n$ to $C^n$ 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. | | Source: | arXiv, math.CV/0305162 | | Services: | Forum | Review | PDF | Favorites | |
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