Properties of resonant states for generic smooth expanding maps

2026/07/28 by Malo Jézéquel
#math.DS

paper · pdf

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.

Citations

• Resonances for rational Anosov maps on the torus
• The linear request problem
• Lower bounds for the Ruelle spectrum of analytic expanding circle maps
• Linear response, or else
• Spectral structure of transfer operators for expanding circle maps
• Explicit eigenvalue estimates for transfer operators
• On the Ruelle eigenvalue sequence

Related

• Some Remarks on Expanding Maps
• Ground States are generically a Periodic Orbit
• Existence, uniqueness and stability of equilibrium states for non-uniformly expanding maps
• Regularity, linear response formula and differentiability of the free energy for non-uniformly expanding local homeomorphisms
• Equilibrium states for natural extensions of non-uniformly expanding\n local homeomorphisms