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We consider a piecewise analytic real expanding map f: [0, 1] → [0, 1] of degree d which preserves orientation, and a real analytic positive potential g: [0, 1] → ℝ. We assume the map and the potential have a complex analytic extension to a neighborhood of the interval in the complex plane. We also assume log g is well defined for this extension.

Ergodic transport theory and piecewise analytic subactions for analytic dynamics