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7 papers
Quasi-periodic solutions to the incompressible Euler equations in dimensions two and higher
Alberto Enciso, Daniel Peralta-Salas, Francisco Torres de Lizaur
Building on the work of Crouseilles and Faou on the 2D case, we construct quasi-periodic solutions to the incompressible Euler equations with periodic boundary condition…
Distribution symmetry of toral eigenfunctions
Ángel D. Martínez, Francisco Torres de Lizaur
In this paper we study a number of conjectures on the behavior of the value distribution of eigenfunctions. On the two dimensional torus we observe that the symmetry conjecture hol…
Chaos in the incompressible Euler equation on manifolds of high dimension
Francisco Torres de Lizaur
We construct finite dimensional families of non-steady solutions to the Euler equations, existing for all time, and exhibiting all kinds of qualitative dynamics in the phase space,…
Periodic orbits of analytic Euler fields on 3-manifolds
Francisco Torres de Lizaur
On any closed Riemannian 3-manifold which is not a torus bundle, every nonvanishing analytic solution of the stationary Euler equations has a periodic trajectory. This result is or…
High-energy eigenfunctions of the Laplacian on the torus and the sphere with nodal sets of complicated topology
Alberto Enciso, Daniel Peralta-Salas, Francisco Torres de Lizaur
Let be an oriented compact hypersurface in the round sphere or in the flat torus , . In the case of the torus, is further assumed to b…
Geometric structures in the nodal sets of eigenfunctions of the Dirac operator
Francisco Torres de Lizaur
We show that, in round spheres of dimension , for any given collection of codimension 2 smooth submanifolds of arbitrarily complicated topol…