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arXiv · 2410.07532

A Maximum Modulus Theorem for functions admitting Stokes phenomena, and specific cases of Dulac's Theorem

Jesús Palma-Márquez·Melvin Yeung
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Abstract

We study large classes of real-valued analytic functions that naturally emerge in the understanding of Dulac's problem, which addresses the finiteness of limit cycles in planar differential equations. Building on a Maximum Modulus-type result we got, our main statement essentially follows. Namely, for any function belonging to these classes, the following dichotomy holds: either it has isolated zeros or it coincides with the identity. As an application, we prove that the non-accumulation of limit cycles holds around a specific class of the so-called superreal polycycles.

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Jesús Palma-Márquez, Melvin Yeung. 2024-10-10. A Maximum Modulus Theorem for functions admitting Stokes phenomena, and specific cases of Dulac's Theorem. https://arxiv.org/abs/2410.07532

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