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math.DS2026
Fourier decay of equilibrium states and the Fibonacci Hamiltonian
Gaétan Leclerc
We show power Fourier decay for equilibrium states of nonlinear, area preserving, smooth Axiom-A diffeomorphisms on surfaces. This implies positivity of the lower Fourier dimension…
math.DS2026
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 i…
math.DS2024
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…