Böttcher coordinates

Open problems in local discrete holomorphic dynamics

“…The postcritical set of a homogeneous map is a cone; thus a superattracting germ f can be topologically (respectively, holomorphically) locally conjugated to a homogeneous map only if its postcritical set is a topological (respectively, analytic) cone, that is the image of a standard cone under a local homeomorphism (respectively, biholomorphism). Buff, Epstein and Koch [22] have proved that this condition is also sufficient when the homogeneous map is non-degenerate:…”

“…Theorem 11 (Buff-Epstein-Koch 2011 [22]) Let f ∈ End(C n , O) be a superattracting germ, and let H: C n → C n be the first non-vanishing term, of degree c = c(f ), in the homogeneous expansion of f . Assume that H is nondegenerate, that is H −1 (O) = {O}.…”

On Böttcher coordinates and quasiregular maps

“…We also mention that Böttcher coordinates have been studied in the setting of several complex variables [6].…”