Exploració per autor "Cardona Aguilar, Robert"
Ara es mostren els items 1-14 de 14
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Computability and Beltrami fields in Euclidean space
(2022-11-12)
Article
Accés obertIn 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 equations in Euclidean space, of Beltrami ... -
Constructing Turing complete Euler flows in dimension 3
(2021-05-11)
Article
Accés obertCan every physical system simulate any Turing machine? This is a classical problem which is intimately connected with the undecidability of certain physical phenomena. Concerning fluid flows, Moore asked in [15] if ... -
Euler flows and singular geometric structures
(Royal Society, 2019)
Article
Accés obertTichler proved in [24] that a manifold admitting a smooth non vanishing and closed one-form bers over a circle. More generally a manifold admitting k independent closed one-forms bers over a torus Tk. In this article we ... -
Integrable Systems in singular symplectic manifolds
(Universitat Politècnica de Catalunya, 2018-07)
Projecte Final de Màster Oficial
Accés obertEn aquest treball es presenten les nocions de geometria simplèctica, de Poisson i b-simplèctica. En cada cas està demostrat un teorema de Arnold-Liouville per a sistemes integrables. Desprès de demostrar una part d'aquests ... -
Integrable systems on singular symplectic manifolds: from local to global
(2021-09-22)
Article
Accés obertIn this article, we consider integrable systems on manifolds endowed with symplectic structures with singularities of order one. These structures are symplectic away from a hypersurface where the symplectic volume goes ... -
Integrable systems on singular symplectic manifolds: from local to global
(2020-09)
Report de recerca
Accés obertIn this article we consider integrable systems on manifolds endowed with singular sym-plectic structures of order one. By singular symplectic structures of order one we mean structureswhich are symplectic away from an ... -
Looking at Euler flows through a contact mirror: universality and undecidability
(European Mathematical Society (EMS), 2021)
Text en actes de congrés
Accés obertThe dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. In recent papers by Cardona, Miranda, and Peralta- Salas, several unknown facets of the Euler flows ... -
On the volume elements of a manifold with transverse zeroes
(Springer, 2019)
Article
Accés obertMoser proved in 1965 in his seminal paper [15] 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 their associated cohomology classes in ... -
Reeb embeddings and universality of Euler flows
(Springer, 2021)
Capítol de llibre
Accés obertWe use a new geometrical approach to the universality of Euler flows. By proving flexibility results on embeddings for Reeb flows in contact topology, we deduce some new universal properties for Euler flows. As a byproduct, ... -
Symplectic toric manifolds, Delzant theorem and integrable sytems
(Universitat Politècnica de Catalunya, 2017-07)
Treball Final de Grau
Accés obertEn aquesta tesi estudiarem la relació entre les varietats simplèctiques tòriques i els sistemes integrables. Per això, presentem en primer lloc tots els preliminars necessaris de geometria simplèctica. Després presentem ... -
The geometry and topology of steady Euler flows, integrability and singular geometric structures
(Universitat Politècnica de Catalunya, 2021-05-26)
Tesi
Accés obertIn this thesis, we make a deep investigation of the geometry and dynamics of several objects (singular or not) appearing in nature. The main goal is to study rigidity versus flexibility dynamical behavior of the objects ... -
Turing universality of the incompressible Euler equations and a conjecture of Moore
(2021-08-24)
Article
Accés obertIn 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 Turing machine with a given input is equivalent ... -
Universality of Euler flows and flexibility of Reeb embeddings
(2019-11-05)
Report de recerca
Accés obertThe 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 existence problem for the Euler and Navier ... -
Universality of Euler flows and flexibility of Reeb embeddings
(Elsevier, 2023-09-01)
Article
Accés obertThe dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. Recently, Tao [38], [39] launched a programme to address the global existence problem for the Euler and ...
