5 problems

Let $u$ be a parameter and let $boldsymbol{\mathcal D}( u,1)$ denote the corresponding set of frequencies. For $omegainmathcal D(nu,1)$, consider the Lindstedt series … of quasi-pe…

Let $\mathbb H_n$ be the Heisenberg group, let $\gamma^{s}_{\mathbf{X},L^2}(\mathbb H_n)$ and $\gamma^{(s)}_{\mathbf{X},L^2}(\mathbb H_n)$ be the corresponding sub-Laplacian Gevrey…

Let $u_{\varepsilon}$ denote the parametrization of the quasi-periodic invariant circle for the dissipative standard map, viewed as a function of the complex parameter…

In the Sitnikov problem, let $e\in(0,1)$ denote the eccentricity, and in the restricted planar three-body problem (RPTBP), let $\mu\in(0,1/2]$ denote the mass parameter. An invaria…

Let $0<\nu<1$ be the order of the singular cross section kernel, and let $f$ be a weak solution of the non-cutoff homogeneous Boltzmann equation in $\mathbb{R}^d$ with initial datu…