7 problems

Let $X$ be a complex manifold endowed with a Riemannian metric, and let $f\colon X\to X$ be an automorphism acting hyperbolically on an invariant compact subset $K\subset X$. For…

Consider the critical focusing nonlinear Schrödinger equation in one spatial dimension and its standing-wave blow-up solutions. The generalized root space of the linearized operato…

Consider the stochastic reaction–diffusion equation on a bounded smooth domain $\mathcal D\subset\mathbb R^d$ with Dirichlet boundary conditions, obtained from (4.10) by replacing…

Stable-manifold conjecture. Such initial data are globally well-posed under the nonlinear Schrödinger dynamics if and only if $u_0\notin\mathcal{W}^s(0)$.

Let an analytic and generic unfolding of a saddle-node be given, with the results of the paper established under the technical assumptions $a^0>-2$ and…

Let $F$ be a holomorphic automorphism acting hyperbolically on a compact invariant set $K$, and let $W^s(K)$ be a stable manifold arising from this action. Stable-manifold Euclidea…

Let $B$ be the unit ball in $\mathbb{C}^d$, and let $(f_n\colon B\to B)_{n\in\mathbb{N}}$ be a sequence of holomorphic maps fixing $0$ and satisfying … for some…