Výsledky vyhledávání - "Leclerc, Gaétan"

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Nonlinearity, Fractals, Fourier decay -- Harmonic analysis of equilibrium states for hyperbolic dynamical systems

Autor: Leclerc, Gaétan

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 fractal geometry: the Fourier dimension, the thermodynamical formalism

Externí odkaz: http://arxiv.org/abs/2410.15476

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Spectrally cut-off GFF, regularized $\Phi^4$ measure, and reflection positivity

Autor: Bailleul, Ismael, Dang, Nguyen Viet, Ferdinand, Léonard, Leclerc, Gaëtan, Lin, Jiasheng

We argue that the spectrally cut-off Gaussian free field $\Phi_\Lambda$ on a compact Riemannian manifold or on $\mathbb{R}^n$ cannot satisfy the spatial Markov property. Moreover, when the manifold is reflection positive, we show that $\Phi_\Lambda$

Externí odkaz: http://arxiv.org/abs/2312.15511

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Fourier decay of equilibrium states on hyperbolic surfaces

Autor: Leclerc, Gaétan

Let $\Gamma$ be a (convex-)cocompact group of isometries of the hyperbolic space $\mathbb{H}^d$, let $M := \mathbb{H}^d/\Gamma$ be the associated hyperbolic manifold, and consider a real valued potential $F$ on its unit tangent bundle $T^1 M$. Under

Externí odkaz: http://arxiv.org/abs/2307.10755

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Fourier decay of equilibrium states for bunched attractors

Autor: Leclerc, Gaétan

Let $M$ be a closed manifold, and let $f:M \rightarrow M$ be a $C^{2+\alpha}$ Axiom A diffeomorphism. Suppose that $f$ has an attractor $\Omega$ with codimension 1 stable lamination. Under a generic nonlinearity condition and a suitable bunching cond

Externí odkaz: http://arxiv.org/abs/2301.10623

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On oscillatory integrals with H\'older phases

Autor: Leclerc, Gaétan

We exhibit a family of autosimilar H\"older maps that satisfies a fractal version of the Van Der Corput Lemma, despite not being absolutely continuous. The result is a direct consequence of a recent work of Sahlsten and Steven arXiv:2009.01703, which

Externí odkaz: http://arxiv.org/abs/2211.08088

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Julia sets of hyperbolic rational maps have positive Fourier dimension

Autor: Leclerc, Gaétan

Let $f:\widehat{\mathbb{C}}\rightarrow \widehat{\mathbb{C}}$ be a hyperbolic rational map of degree $d \geq 2$, and let $J \subset \mathbb{C}$ be its Julia set. We prove that $J$ always has positive Fourier dimension. The case where $J$ is included i

Externí odkaz: http://arxiv.org/abs/2112.00701

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