15 citations · 19 across the 7 of their papers we have counts for
7 papers
-Poisson geometry, coisotropic submanifolds, and clean intersection points
Robert Cardona, Fabio Gironella
In this work, we initiate the study of rigidity and non-rigidity phenomena for Poisson homeomorphisms, defined as uniform -limits of Poisson diffeomorphisms. First, we prove t…
On dynamical invariants of coadjoint orbits of 3D volume-preserving diffeomorphisms
Robert Cardona, Julian Chaidez, Francisco Torres de Lizaur
The helicity, or asymptotic linking number, is a functional of exact volume-preserving vector fields on 3-manifolds, invariant under volume-preserving transformations. It is known…
Towards a Fluid computer
Robert Cardona, Eva Miranda, Daniel Peralta-Salas
In 1991, Moore [20] raised a question about whether hydrodynamics is capable of performing computations. Similarly, in 2016, Tao [25] asked whether a mechanical system, including a…
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…
Contact type solutions and non-mixing of the 3D Euler equations
Robert Cardona, Francisco Torres de Lizaur
We prove that on any closed Riemannian three-manifold the time-dependent Euler equations are non-mixing on the space of smooth volume-preserving vector fields endowed with…
Asymmetry of MHD equilibria for generic adapted metrics
Robert Cardona, Nathan Duignan, David Perrella
Ideal magnetohydrodynamic (MHD) equilibria on a Riemannian 3-manifold satisfy the stationary Euler equations for ideal fluids. A stationary solution admits a large set of ``ada…
Computability and Beltrami fields in Euclidean space
Robert Cardona, Eva Miranda, Daniel Peralta-Salas
In this article, we pursue our investigation of the connections between the theory of computation and hydrodynamics. We prove the existence of stationary solutions of the Euler equ…