Local analytic conjugacy of semi-hyperbolic mappings in two variables, in the non-Archimedean setting (Q2888827)

The authors study germs of locally invertible analytic mappings of a two-dimensional space over a non-Archimedean field of characteristic 0. Two such germs are called formally equivalent if they are conjugate in the group of invertible formal power series. In general, formally equivalent mappings need not be analytically equivalent; see [\textit{M. Herman} and \textit{J.-C. Yoccoz}, ``Generalizations of some theorems of small divisors to non Archimedean fields'', Lect. Notes Math. 1007, 408--447 (1983; Zbl 0528.58031)]. The authors prove this implication for semi-hyperbolic mappings, that is, for those whose Jacobians have eigenvalues \(\lambda_1\) and \(\lambda_2\) such that \(\lambda_1=1\), \(|\lambda_2|\neq 1\). The technique is a further development of that from the authors' earlier paper [``A \(p\)-adic approach to local analytic dynamics: analytic conjugacy of analytic maps tangent to the identity'', Ann. Fac. Sci. Toulouse, Math. (6) 18, No. 3, 611--634 (2009; Zbl 1185.37210)].