4 papers
A note on the RAGE Theorem and phase-averaged dispersion for the Fibonacci Hamiltonian
Gaétan Leclerc
We find a weaker condition on spectral measures, "eventual absolute continuity", that ensure quantum delocalization as in the RAGE Theorem in the case of purely absolutely continuo…
Fourier decay in parabolic systems with overlaps
Gaétan Leclerc, Sampo Paukkonen, Tuomas Sahlsten
We establish power Fourier decay for equilibrium states of parabolic iterated function systems with overlaps satisfying a multiscale nonlinearity condition. This class in…
Nonlinearity, Fractals, Fourier decay -- Harmonic analysis of equilibrium states for hyperbolic dynamical systems
Gaétan Leclerc
This is my (reviewed) PhD manuscript. It contains 6 Chapters, which contains mostly already published work, except for Chapter 5 which is new. Chapter 1 introduce basic notions on…
On oscillatory integrals with Hölder phases
Gaétan Leclerc
We exhibit a family of autosimilar Hölder maps that satisfies a fractal version of the Van Der Corput Lemma, despite not being absolutely continuous. The result is a direct consequ…