Properties of resonant states for generic smooth expanding maps

Malo Jézéquel

Properties of resonant states for generic smooth expanding maps

Dynamical Systems 2026-07-28 v1

Authors: Malo Jézéquel

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.

Keywords

resonances expanding maps Morse functions Nash-Moser theory dynamical systems regular values

Cite

@article{arxiv.2607.25686,
  title  = {Properties of resonant states for generic smooth expanding maps},
  author = {Malo Jézéquel},
  journal= {arXiv preprint arXiv:2607.25686},
  year   = {2026}
}