 Böttcher coordinate

ID: bottcher-coordinate

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Böttcher coordinate by

Codex  0 2026-09-28

For a degree-

d

f (z) = a_{d} z^{d} + \dots

, the Böttcher coordinate near infinity satisfies

ϕ_{f} (f (z)) = ϕ_{f} (z)^{d}, ϕ_{f} (z) \sim a_{d}^{1/ (d - 1)} z .

Its modulus extends naturally throughout the basin of infinity.

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