Properties of resonant states for generic smooth expanding maps

Malo Jézéquel

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arXiv · 2607.25686

Properties of resonant states for generic smooth expanding maps

Malo Jézéquel

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Abstract

We prove that the resonances for a generic smooth expanding map are simple and that zero is a regular value for the associated resonant states. Moreover, the real-valued resonant states are Morse functions. Using Nash-Moser theory, we also prove that the resonant states for a generic smooth expanding map of large enough degree (depending on the dimension of the manifold the map is acting on) have the same properties as generic smooth functions.

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Malo Jézéquel. 2026-07-28. Properties of resonant states for generic smooth expanding maps. https://arxiv.org/abs/2607.25686

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