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arXiv · 2506.19562

Monotonicity properties of hyperbolic projections in holomorphic iteration

Argyrios Christodoulou·Konstantinos Zarvalis
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Abstract

We consider hyperbolic projections of orbits of holomorphic self-maps of the unit disc, onto curves landing on the unit circle with a given angle. We show that under certain, necessary, assumptions, the projections exhibit monotonicity properties akin to those present in continuous dynamics. Our techniques are purely hyperbolic-geometric in nature and provide the general framework for analysing projections of arbitrary sequences onto curves.

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Argyrios Christodoulou, Konstantinos Zarvalis. 2025-06-24. Monotonicity properties of hyperbolic projections in holomorphic iteration. https://arxiv.org/abs/2506.19562

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