Recurrent Inversion Formulas
| dc.creator | Zhao, Wenhua | |
| dc.date | 2003-05-12 | |
| dc.date | 2004-02-19 | |
| dc.date.accessioned | 2026-07-07T06:35:37Z | |
| dc.date.available | 2026-07-07T06:35:37Z | |
| dc.description | 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 $d\geq 2$. 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. | |
| dc.description | Latex2e, 17 pages. A mistake was cirrecred. References were updated | |
| dc.identifier | https://arxiv.org/abs/math/0305162 | |
| dc.identifier | http://arxiv.org/abs/math/0305162 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99850 | |
| dc.subject | Complex Variables | |
| dc.subject | Mathematical Physics | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 32H02, 14R15 | |
| dc.title | Recurrent Inversion Formulas | |
| dc.type | text |