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<p>This paper, based upon an unpublished manuscript by Maurice Heins, answers a question posed by Valiron about the dynamics of parabolic self-maps of the unit disk in the complex plane, considerably simplifying arguments previously used for answering the same question. The main new tool introduced is the notion of left straightening of a sequence of iterates, which can be effectively employed for studying the hyperbolic step of a parabolic map.</p>

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Parabolic dynamics according to Maurice Heins

  • 期刊论文

  • 发表日期：

    2025年10月6日

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  • Marco Abate

摘要

This paper, based upon an unpublished manuscript by Maurice Heins, answers a question posed by Valiron about the dynamics of parabolic self-maps of the unit disk in the complex plane, considerably simplifying arguments previously used for answering the same question. The main new tool introduced is the notion of left straightening of a sequence of iterates, which can be effectively employed for studying the hyperbolic step of a parabolic map.