O. Khalil

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20242026

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math.DS2026

Measure rigidity and equidistribution for fractal carpets

Osama Khalil, Manuel Luethi, Barak Weiss

Let $I^¸$ be a Bernoulli measure which is stationary for a random walk generated by finitely many contracting rational affine dilations of $R^{d}$ , and let $\mathcal{K} = \ma…

math.DS2025

Veech Surfaces and Expanding Twist Tori on Moduli Spaces of Abelian Differentials

Jon Chaika, Osama Khalil

Let $(M, I ¨ )$ be a translation surface such that every leaf of its horizontal foliation is either closed, or joins two zeros of $I ¨ $ . Then, $M$ decomposes as a union of horizontal E…

math.DS2024

Fourier Decay from $L^{2}$ -Flattening

Simon Baker, Osama Khalil, Tuomas Sahlsten

We develop a unified approach for establishing rates of decay for the Fourier transform of a wide class of dynamically defined measures. Among the key features of the method is the…

math.DS2024

Polynomial Fourier Decay For Patterson-Sullivan Measures

Osama Khalil

We show that the Fourier transform of Patterson-Sullivan measures associated to convex cocompact groups of isometries of real hyperbolic space decays polynomially quickly at infini…

Measure rigidity and equidistribution for fractal carpets

Veech Surfaces and Expanding Twist Tori on Moduli Spaces of Abelian Differentials

Fourier Decay from L2-Flattening

Polynomial Fourier Decay For Patterson-Sullivan Measures

Fourier Decay from $L^{2}$ -Flattening