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<p>We show that every cubic Blaschke product has a unique hyperbolic inflection point in the unit disk and, moreover, this point lies at the hyperbolic midpoint of the two critical points. Using this structure result for cubic Blaschke products, we give an explicit expression in terms of the parameters which determines when cubic Blaschke products are elliptic, parabolic, or hyperbolic.</p>

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On Cubic Blaschke Products

  • 期刊论文

  • 发表日期：

    2026年5月8日

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  • Alastair N. Fletcher,
  • Alexandra Hill

摘要

We show that every cubic Blaschke product has a unique hyperbolic inflection point in the unit disk and, moreover, this point lies at the hyperbolic midpoint of the two critical points. Using this structure result for cubic Blaschke products, we give an explicit expression in terms of the parameters which determines when cubic Blaschke products are elliptic, parabolic, or hyperbolic.