For regular polynomial endomorphisms of C^n and endomorphisms of P^n, any family of as many multipliers as the moduli dimension, from distinct cycles of period at least four (or five in one exceptional case), is algebraically independent.
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Independence of multipliers in several variables complex dynamics
For regular polynomial endomorphisms of C^n and endomorphisms of P^n, any family of as many multipliers as the moduli dimension, from distinct cycles of period at least four (or five in one exceptional case), is algebraically independent.