Eva Miranda
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View article: Universality in computable dynamical systems: old and new
Universality in computable dynamical systems: old and new Open
The relationship between computational models and dynamics has captivated mathematicians and computer scientists since the earliest conceptualizations of computation. Recently, this connection has gained renewed attention, fueled by T. Tao…
View article: Universality in computable dynamical systems: Old and new
Universality in computable dynamical systems: Old and new Open
The relationship between computational models and dynamics has captivated mathematicians and computer scientists since the earliest conceptualizations of computation. Recently, this connection has gained renewed attention, fueled by T. Tao…
View article: Turing complete Navier-Stokes steady states via cosymplectic geometry
Turing complete Navier-Stokes steady states via cosymplectic geometry Open
In this article, we construct stationary solutions to the Navier-Stokes equations on certain Riemannian $3$-manifolds that exhibit Turing completeness, in the sense that they are capable of performing universal computation. This universali…
View article: Cosymplectic Chern--Hamilton conjecture
Cosymplectic Chern--Hamilton conjecture Open
In this paper, we study the Chern-Hamilton energy functional on compact cosymplectic manifolds, fully classifying in dimension 3 those manifolds admitting a critical compatible metric for this functional. This is the case if and only if ei…
View article: Topological Kleene Field Theories as a model of computation
Topological Kleene Field Theories as a model of computation Open
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 partial recursive functions and drawing parallels with Topolo…
View article: Which singular tangent bundles are isomorphic?
Which singular tangent bundles are isomorphic? Open
Logarithmic and $b$-tangent bundles provide a versatile framework for addressing singularities in geometry. Introduced by Deligne and Melrose, these modified bundles resolve singularities by reframing singular vector fields as well-behaved…
View article: Uso del método de Monte Carlo y estadística inferencial en la estimación de áreas geográficas Casos de Bogotá y Burlington
Uso del método de Monte Carlo y estadística inferencial en la estimación de áreas geográficas Casos de Bogotá y Burlington Open
This article seeks, through the statistical implementation of the Monte Carlo method, to determine geographic surface areas, taking the cities of Bogot´a and Burlington as case studies using their shapefiles.To fulfill this purpose, the R …
View article: The two-boost problem and Lagrangian Rabinowitz Floer homology
The two-boost problem and Lagrangian Rabinowitz Floer homology Open
The two-boost problem in space mission design asks whether two points of phase space can be connected with the help of two boosts of given energy. We provide a positive answer for a class of systems related to the restricted three-body pro…
View article: E-structures and almost regular Poisson manifolds
E-structures and almost regular Poisson manifolds Open
In recent years, $b$-symplectic manifolds have become important structures in the study of symplectic geometry, serving as Poisson manifolds that retain symplectic properties away from a hypersurface. Inspired by this rich landscape, $E$-s…
View article: Towards a Fluid computer
Towards a Fluid computer Open
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 fluid flow, can simulate a universal Turing machine. In th…
View article: The Arnold conjecture for singular symplectic manifolds
The Arnold conjecture for singular symplectic manifolds Open
In this article, we study the Hamiltonian dynamics on singular symplectic manifolds and prove the Arnold conjecture for a large class of $$b^m$$ -symplectic manifolds. Novel techniques are introduced to associate smooth symplectic form…
View article: Topological entropy of Turing complete dynamics (with an appendix by Ville Salo)
Topological entropy of Turing complete dynamics (with an appendix by Ville Salo) Open
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 "regular Turing machines" (which includes most of the examples of uni…
View article: Darboux, Moser and Weinstein theorems for prequantum systems
Darboux, Moser and Weinstein theorems for prequantum systems Open
We establish analogs of the Darboux, Moser and Weinstein theorems for prequantum systems. We show that two prequantum systems on a manifold with vanishing first cohomology, with symplectic forms defining the same cohomology class and homot…
View article: An equivariant Reeb–Beltrami correspondence and the Kepler–Euler flow
An equivariant Reeb–Beltrami correspondence and the Kepler–Euler flow Open
We prove that the correspondence between Reeb and Beltrami vector fields presented in Etnyre & Ghrist (Etnyre, Ghrist 2000 Nonlinearity 13 , 441–458 ( doi:10.1088/0951-7715/13/2/306 )) can be made equivariant whenever additional symmetries…
View article: A counterexample to the singular Weinstein conjecture
A counterexample to the singular Weinstein conjecture Open
In this article, we study the dynamical properties of Reeb vector fields on b-contact manifolds. We show that in dimension 3, the number of so-called singular periodic orbits can be prescribed. These constructions illuminate some key prope…
View article: From $$2N$$ to Infinitely Many Escape Orbits
From $$2N$$ to Infinitely Many Escape Orbits Open
—In this short note, we prove that singular Reeb vector fields associated with generic b-contact forms on three dimensional manifolds with compact embedded critical surfaces have either (at least) 2N or an infinite number of escape orbits,…
View article: Looking at Euler flows through a contact mirror: Universality and undecidability
Looking at Euler flows through a contact mirror: Universality and undecidability Open
The dynamics of an inviscid and incompressible fluid flow on a Riemannian\nmanifold is governed by the Euler equations. In recent papers [5, 6, 7, 8]\nseveral unknown facets of the Euler flows have been discovered, including\nuniversality …
View article: Constructions of <i>b</i>-semitoric systems
Constructions of <i>b</i>-semitoric systems Open
In this article, we introduce b-semitoric systems as a generalization of semitoric systems, specifically tailored for b-symplectic manifolds. The objective of this article is to furnish a collection of examples and investigate the distinct…
View article: Reduction theory for singular symplectic manifolds and singular forms on moduli spaces
Reduction theory for singular symplectic manifolds and singular forms on moduli spaces Open
© 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license
View article: An equivariant Reeb-Beltrami correspondence and the Kepler-Euler flow
An equivariant Reeb-Beltrami correspondence and the Kepler-Euler flow Open
We prove that the correspondence between Reeb and Beltrami vector fields can be made equivariant whenever additional symmetries of the underlying geometric structures are considered. As a corollary of this correspondence, we show that ener…
View article: Hamiltonian facets of classical gauge theories on <i>E</i>-manifolds
Hamiltonian facets of classical gauge theories on <i>E</i>-manifolds Open
Manifolds with boundary, with corners, b -manifolds and foliations model configuration spaces for particles moving under constraints and can be described as E -manifolds. E -manifolds were introduced in Nest and Tsygan (2001 Asian J. Math.…
View article: Constructions of b-semitoric systems
Constructions of b-semitoric systems Open
In this article, we introduce $b$-semitoric systems as a generalization of semitoric systems, specifically tailored for $b$-symplectic manifolds. The objective of this article is to furnish a collection of examples and investigate the dist…
View article: From 2N to infinitely many escape orbits
From 2N to infinitely many escape orbits Open
In this short note, we prove that singular Reeb vector fields associated with generic $b$-contact forms have either (at least) $2N$ or an infinite number of escape orbits, where $N$ denotes the number of connected components of the critica…
View article: Bohr–Sommerfeld quantization of $b$-symplectic toric manifolds
Bohr–Sommerfeld quantization of $b$-symplectic toric manifolds Open
We define the Bohr-Sommerfeld quantization via T -modules for a b-symplectic toric manifold and show that it coincides with the formal geometric quantization of [Victor W. Guillemin, Eva Miranda, and Jonathan Weitsman. On geometric quantiz…