In any degenerating one-parameter family of rational maps, either all periodic multipliers stay uniformly bounded or almost all of them blow up at a power rate, and degenerating cubic families always contain a short repelling cycle with blowing-up multiplier.
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Blow-up of multipliers in meromorphic families of rational maps
In any degenerating one-parameter family of rational maps, either all periodic multipliers stay uniformly bounded or almost all of them blow up at a power rate, and degenerating cubic families always contain a short repelling cycle with blowing-up multiplier.