(Unmarked) Length spectral rigidity for expanding circle maps
Vortrag von Prof. Dr. Kostiantyn Drach
Sprecher eingeladen von: Prof. Dr. Corinna Ulcigrai
Datum: 09.04.25 Zeit: 13.30 - 14.30 Raum: ETH HG G 19.1
For a smooth expanding map of the circle, its (unmarked) length spectrum is defined as the set of logarithms of multipliers along all periodic orbits. This set is analogous to the set of lengths of all closed geodesics on negatively curved surfaces -- the classical length spectrum. In the talk, I will present a length spectral rigidity result for expanding circle maps. Namely, I will show that a smooth expanding circle map, under certain assumptions on the sparsity of its length spectrum, cannot be perturbed with an arbitrarily small smooth perturbation (depending on the map) so that the length spectrum stays the same. The proof uses the Whitney extension theorem, a quantitative Livcis-type theorem, and a novel iterative scheme. This is joint work with Vadim Kaloshin.