10 papers
Computable functions as Reeb flows
Kai Cieliebak, Ãngel González-Prieto, Eva Miranda
We prove that, given any contact -manifold and any computable function , there exists a defining contact form and a Poincaré section o…
Two-Dimensional Billiards Are Turing Complete
Eva Miranda, Isaac Ramos
We show that two-dimensional billiard systems can simulate universal Turing machines. Billiards serve as idealized models of particle motion with elastic reflections and arise natu…
Which singular tangent bundles are isomorphic?
Eva Miranda, Pablo Nicolás
Logarithmic and -tangent bundles provide a versatile framework for addressing singularities in geometry. Introduced by Deligne and Melrose, these modified bundles resolve singul…
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…
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…
Universality in computable dynamical systems: Old and new
Ãngel González-Prieto, Eva Miranda, Daniel Peralta-Salas
The relationship between computational models and dynamics has captivated mathematicians and computer scientists since the earliest conceptualizations of computation. Recently, thi…