4 papers · 1 filter
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…
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…
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…