Mathematics – Dynamical Systems
Scientific paper
2011-11-08
Contemporary matematics, Amer. Math. Soc., Vol. 508, pp. 89-109, 2010
Mathematics
Dynamical Systems
Scientific paper
We continue the study in [21] of the linearizability near an indif- ferent fixed point of a power series f, defined over a field of prime characteristic p. It is known since the work of Herman and Yoccoz [13] in 1981 that Siegel's linearization theorem [27] is true also for non- Archimedean fields. However, they also showed that the condition in Siegel's theorem is 'usually' not satisfied over fields of prime character- istic. Indeed, as proven in [21], there exist power series f such that the associated conjugacy function diverges. We prove that if the degrees of the monomials of a power series f are divisible by p, then f is analyt- ically linearizable. We find a lower (sometimes the best) bound of the size of the corresponding linearization disc. In the cases where we find the exact size of the linearization disc, we show, using the Weierstrass degree of the conjugacy, that f has an indifferent periodic point on the boundary. We also give a class of polynomials containing a monomial of degree prime to p, such that the conjugacy diverges.
No associations
LandOfFree
Divergence and convergence of conjugacies in non-Archimedean dynamics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Divergence and convergence of conjugacies in non-Archimedean dynamics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Divergence and convergence of conjugacies in non-Archimedean dynamics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-54323