Quasiconformality and invertibility of transformations in non archimedean vector spaces

AbstractThe paper treats functions which in a finite dimensional normed space over a field with a non archimedean valuation possess a certain simple quasilinearity property. The first principal result states that these functions are quasiconformal in certain balls. The second result is an inverse function theorem which characterizes in a simple way the images of the functions considered. An existence theorem for quasilinear functions is then provided as well. The paper closes with a presentation of two algorithms for the numerical inversion of quasilinear functions