15 papers
Piecewise smooth stationary Euler flows with support in a neighborhood of a helix
Daniel Peralta-Salas, Jie Wan
We construct stationary solutions of the three-dimensional incompressible Euler equations with helical symmetry and support in a neighborhood of a helix. The solutions are piecewis…
A symmetry theorem for localizable steady solutions of the 3D Euler equations
Daniel Peralta-Salas, Radu Slobodeanu
A steady Euler flow is localizable if the pressure function is constant along its stream lines. This property was used by Gavrilov to construct the first smooth compactly supported…
Topological entropy of Turing complete dynamics
Renzo Bruera, Robert Cardona, Eva Miranda +2
We explore the relationship between Turing completeness and topological entropy of dynamical systems. We first prove that a natural class of Turing machines that we call "branching…
Hölder continuous dissipative solutions of ideal MHD with nonzero helicity
Alberto Enciso, Javier Peñafiel-Tomás, Daniel Peralta-Salas
We prove the existence of weak solutions to the 3D ideal MHD equations, of class with , for which the total energy and the cross helicity (i.e., the so-called ElsÃ…
Topological Kleene Field Theories as a model of computation
Ãngel González-Prieto, Eva Miranda, Daniel Peralta-Salas
In this article, we establish the foundations of a computational field theory, which we term Topological Kleene Field Theory (TKFT), inspired by Stephen Kleene's seminal work on pa…
Low-energy dynamics in generic potential fields: Hyperbolic periodic orbits and non-ergodicity
Alberto Enciso, Manuel Garzón, Daniel Peralta-Salas
We prove that, on each low energy level, the natural Hamiltonian system defined by a generic smooth potential on exhibits an arbitrarily high number of hyperbolic pe…