152 citations · 626 across the 48 of their papers we have counts for
55 papers
Equivariant cosymplectic geometry
Eva Miranda, Pablo Nicolás
Cosymplectic manifolds provide a natural geometric framework for codimension-one symplectic foliations and arise throughout geometry and mathematical physics. We develop an equivar…
Hamiltonian group actions in cosymplectic geometry
Eva Miranda, Pablo Nicolás
We develop a theory of Hamiltonian group actions on cosymplectic manifolds. These odd-dimensional manifolds combine a codimension-one symplectic foliation with a distinguished Reeb…
An equivariant Reeb-Beltrami correspondence and the Kepler-Euler flow
Josep Fontana-McNally, Eva Miranda, Daniel Peralta-Salas
We prove that the correspondence between Reeb and Beltrami vector fields can be made equivariant whenever additional symmetries of the underlying geometric structures are considere…
Constructions of b-semitoric systems
Joaquim Brugués, Sonja Hohloch, Pau Mir +1
In this article, we introduce -semitoric systems as a generalization of semitoric systems, specifically tailored for -symplectic manifolds. The objective of this article is t…
From 2N to infinitely many escape orbits
Josep Fontana-McNally, Eva Miranda, Cédric Oms +1
In this short note, we prove that singular Reeb vector fields associated with generic -contact forms have either (at least) or an infinite number of escape orbits, where $N…
Action-angle coordinates and KAM theory for singular symplectic manifolds
Eva Miranda, Arnau Planas
This monograph explores classification and perturbation problems for integrable systems on a class of Poisson manifolds called -Poisson manifolds. Even if the class of -P…
The Arnold conjecture for singular symplectic manifolds
Joaquim Brugués, Eva Miranda, Cédric Oms
In this article, we study the Hamiltonian dynamics on singular symplectic manifolds and prove the Arnold conjecture for a large class of -symplectic manifolds. Novel technique…
Hamiltonian facets of classical gauge theories on -manifolds
Pau Mir, Eva Miranda, Pablo Nicolás
Manifolds with boundary, with corners, -manifolds and foliations model configuration spaces for particles moving under constraints and can be described as -manifolds. -man…
Singular cotangent models and complexity in fluids with dissipation
Baptiste Coquinot, Pau Mir, Eva Miranda
In this article we analyze several mathematical models with singularities where the classical cotangent model is replaced by a -cotangent model. We provide physical interpretati…
Reduction theory for singular symplectic manifolds and singular forms on moduli spaces
Anastasia Matveeva, Eva Miranda
The investigation of symmetries of b-symplectic manifolds and folded-symplectic manifolds is well-understood when the group under consideration is a torus (see, for instance, [GMPS…
Looking at Euler flows through a contact mirror: Universality and undecidability
Robert Cardona, Eva Miranda, Daniel Peralta-Salas
The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. In recent papers [5, 6, 7, 8] several unknown facets of the E…
Turing universality of the incompressible Euler equations and a conjecture of Moore
Robert Cardona, Eva Miranda, Daniel Peralta-Salas
In this article we construct a compact Riemannian manifold of high dimension on which the time dependent Euler equations are Turing complete. More precisely, the halting of any Tur…
Geometric quantization via cotangent models
Pau Mir, Eva Miranda
In this article we give a universal model for geometric quantization associated to a real polarization given by an integrable system with non-degenerate singularities. This univers…
Constructing Turing complete Euler flows in dimension
Robert Cardona, Eva Miranda, Daniel Peralta-Salas +1
Can every physical system simulate any Turing machine? This is a classical problem which is intimately connected with the undecidability of certain physical phenomena. Concerning f…
On the singular Weinstein conjecture and the existence of escape orbits for -Beltrami fields
Eva Miranda, Cédric Oms, Daniel Peralta-Salas
Motivated by Poincaré's orbits going to infinity in the (restricted) three-body (see [26] and [6]), we investigate the generic existence of heteroclinic-like orbits in a neighbourh…
-Structures on Lie groups and Poisson reduction
Roisin Braddell, Anna Kiesenhofer, Eva Miranda
Motivated by the group of Galilean transformations and the subgroup of Galilean transformations which fix time zero, we introduce the notion of a -Lie group as a pair wh…
Integrable systems on singular symplectic manifolds: From local to global
Robert Cardona, Eva Miranda
In this article we consider integrable systems on manifolds endowed with singular symplectic structures of order one. These structures are symplectic away from an hypersurface wher…
Rigidity of cotangent lifts and integrable systems
Pau Mir, Eva Miranda
In this article we generalize a theorem by Palais on the rigidity of compact group actions to cotangent lifts. We use this result to prove rigidity for integrable systems on symple…
The singular Weinstein conjecture
Eva Miranda, Cédric Oms
In this article, we investigate Reeb dynamics on -contact manifolds, previously introduced in [MiO], which are contact away from a hypersurface but satisfy certain transve…
Universality of Euler flows and flexibility of Reeb embeddings
Robert Cardona, Eva Miranda, Daniel Peralta-Salas +1
The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. Recently, Tao launched a programme to address the global exis…
Euler flows and singular geometric structures
Robert Cardona, Eva Miranda, Daniel Peralta-Salas
Tichler proved that a manifold admitting a smooth closed one-form fibers over a circle. More generally a manifold admitting independent closed one-forms fibers over a torus $T^…
On the volume elements of a manifold with transverse zeroes
Robert Cardona, Eva Miranda
Moser proved in 1965 in his seminal paper that two volume forms on a compact manifold can be conjugated by a diffeomorphism, that is to say they are equivalent, if and only if thei…
A -symplectic slice theorem
Roisin Braddell, Anna Kiesenhofer, Eva Miranda
In this article, motivated by the study of symplectic structures on manifolds with boundary and the systematic study of -symplectic manifolds started in [12], we prove a slice t…
Contact structures with singularities: from local to global
Eva Miranda, Cédric Oms
In this article we introduce and analyze in detail singular contact structures, with an emphasis on -contact structures, which are tangent to a given smooth hypersurface a…