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Böttcher-type potential for the secant map (2508.05847v1)
Published 7 Aug 2025 in math.DS
Abstract: We present a construction of a B\"ottcher-type holomorphic map for the potential of the secant method dynamical system near a root-type fixed point. The modulus of the B\"ottcher-type map extends to be continuous on the entire basin of attraction of the fixed point, and is real-analytic away from the iterated preimages of the fixed point. Using this construction, we show the associated Green's function for the fixed point is pluriharmonic wherever it is finite.
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