Preprints
- The topology of stable electromagnetic structures and Legendrian fields on the 3-sphere (with B. Bode). Preprint, 2023.
- An extension theorem for weak solutions of the 3D incompressible Euler equations and applications to singular flows (with A. Enciso and J. Penafiel). Preprint, 2024.
- Local limits of high-energy eigenfunctions on integrable billiards (with A. Enciso and A. García-Ruiz). Preprint, 2025.
- Topological Kleene field theories: a new model of computation (with A. Gonzalez-Prieto and E. Miranda). Preprint, 2025.
- Steady 3d Euler flows via a topology-preserving convex integration scheme (with A. Enciso and J. Penafiel). Preprint, 2025.
2025
- MHD equilibria with nonconstant pressure in nondegenerate toroidal domains (with A. Enciso and A. Luque). J. Eur. Math. Soc. 27, 2251-2291.
- Obstructions to topological relaxation for generic magnetic fields (with A. Enciso). Arch. Rat. Mech. Anal. 249, 6.
-On the existence of critical compatible metrics on contact 3-manifolds (with Y. Mitsumatsu and R. Slobodeanu). Bull. London Math. Soc. 57, 79-95.
- Isolated steady solutions of the 3D Euler equations (with A. Enciso and W. Kepplinger). Proc. Natl. Acad. Sci. 122, e2414730122.
-Towards a fluid computer (with R. Cardona and E. Miranda). Found. Comput. Math. in press.
- Optimal metrics for the first curl eigenvalue on 3-manifolds (with A. Enciso and W. Gerner). Calc. Var. PDE in press.
2024
- An equivariant Reeb-Beltrami correspondence and the Kepler-Euler flow (with J. Fontana and E. Miranda). Proc. R. Soc. A 480, 20230499.
- Critical point asymptotics for Gaussian random waves with densities of any Sobolev regularity (with A. Enciso and A. Romaniega). Adv. Math. 437, 109450.
- Non-integrability and chaos for natural Hamiltonian systems with a random potential (with A. Enciso and A. Romaniega). Adv. Math. 437, 109448.
- Optimal convex domains for the first curl eigenvalue (with A. Enciso and W. Gerner). Trans. Amer. Math. Soc. 377, 4519-4540.
- Small spheres with prescribed nonconstant mean curvature in Riemannian manifolds (with A. Enciso and A.J. Fernandez). J. Funct. Anal. 286, 110415.
- A counterexample to the singular Weinstein conjecture (with J. Fontana, E. Miranda and C. Oms). Adv. Math. 458, 109998.
- Entanglement of vortices in the Ginzburg-Landau equations for superconductors (with A. Enciso). Comm. Math. Phys. 405, 155-168.
- Beltrami fields with Morse proportionality factor (with M. Vaquero). J. Math. Anal. Appl. 540, 128632.
- Inverse localization and global approximation for some Schrodinger operators on hyperbolic spaces (with A. Enciso and A. García-Ruiz). J. Math. Phys. 65, 062102.
2023
- Localization properties of high-energy eigenfunctions on flat tori (with A. Enciso and A. García-Ruiz). Int. Math. Res. Notices 2023, 20988-21014.
- Computability and Beltrami fields in Euclidean space (with R. Cardona and E. Miranda). J. Math. Pures Appl. 169, 50-81.
- Non-existence of axisymmetric optimal domains with smooth boundary for the first curl eigenvalue (with A. Enciso). Ann. Sc. Norm. Sup. Pisa 24, 343-359.
- Quasi-periodic solutions to the incompressible Euler equations in dimensions two and higher (with A. Enciso and F. Torres de Lizaur). J. Differential Equations 354, 170-182.
- Overdetermined boundary problems with nonconstant Dirichlet and Neumann data (with M. Domínguez-Vázquez and A. Enciso). Anal. & PDE 16, 1989-2003.
- Contact structures and Beltrami fields on the torus and the sphere (with R. Slobodeanu). Indiana Univ. Math. J. 72, 699-730.
- Beltrami fields and knotted vortex structures in incompressible fluid flows (with A. Enciso). Bull. London Math. Soc. 55, 1059-1103.
- Steady Euler flows on R3 with wild and universal dynamics (with P. Berger and A. Florio). Comm. Math. Phys. 401, 937-983.
- Universality of Euler flows and flexibility of Reeb embeddings (with R. Cardona, E. Miranda and F. Presas). Adv. Math. 428, 1-40.
- Beltrami fields exhibit knots and chaos almost surely (with A. Enciso and A. Romaniega). Forum Math. Sigma 11, 1-46
- Limiting measures and energy growth for sequences of solutions to Taubes's Seiberg-Witten equations (with A. Enciso and F. Torres de Lizaur). J. Geom. Anal. 33, 1-53.
- A Liouville-type theorem for the 3D primitive equations (with R. Slobodeanu). Phys. D 453, 133821.
- From 2N to infinitely many escape orbits (with J. Fontana, E. Miranda and C. Oms). Reg. Chaotic Dyn. 28, 498-511.
2022
- On the singular Weinstein conjecture and the existence of escape orbits for b-Beltrami fields (with E. Miranda and C. Oms). Commun. Contemp. Math. 24, 2150076.
- Asymptotics for the nodal components of non-identically distributed monochromatic random waves (with A. Enciso and A. Romaniega). Int. Math. Res. Notices 2022, 774-800.
- Turing universality of the incompressible Euler equations and a conjecture of Moore (with R. Cardona and E. Miranda). Int. Math. Res. Notices 2022, 18092-18109.
- The helicity uniqueness conjecture in 3D hydrodynamics (with B. Khesin and C. Yang). Trans. Amer. Math. Soc. 375, 909-924.
2021
- Piecewise smooth stationay Euler flows with compact support via overdetermined boundary problems (with M. Domínguez-Vázquez and A. Enciso). Arch. Rat. Mech. Anal. 239, 1327-1347.
- Approximation theorems for the Schrodinger equation and quantum vortex reconnection (with A. Enciso). Comm. Math. Phys. 387, 1111-1149.
- A characterization of 3D steady Euler flows using commuting zero-flux homologies (with A. Rechtman and F. Torres de Lizaur). Ergodic Theor. & Dynam. Sys. 41, 2166-2181.
- Energy minimizing Beltrami fields on Sasakian 3-manifolds (with R. Slobodeanu). Int. Math. Res. Notices 2021, 6656-6690.
- A basis of Casimirs in 3D magnetohydrodynamics (with B. Khesin and C. Yang). Int. Math. Res. Notices 2021, 13645-13660.
- Constructing Turing complete Euler flows in dimension 3 (with R. Cardona, E. Miranda and F. Presas). Proc. Natl. Acad. Sci. 118, e2026818118.
2020
- Beltrami fields with hyperbolic periodic orbits enclosed by knotted invariant tori (with A. Enciso and A. Luque). Adv. Math. 373, 107328.
- Global, local and dense non-mixing of the 3D Euler equation (with B. Khesin and S. Kuksin). Arch. Rat. Mech. Anal. 238, 1087-1112.
2019
- Solutions to the overdetermined boundary problem for semilinear equations with position-dependent nonlinearities (with M. Domínguez-Vázquez and A. Enciso). Adv. Math. 351, 718-760.
- Stationary phase methods and the splitting of separatrices (with A. Enciso and A. Luque). Comm. Math. Phys. 368, 1297-1322.
- Approximation theorems for parabolic equations and movement of local hot spots (with A. Enciso and M.A. García-Ferrero). Duke Math. J. 168, 897-939.
- A problem of Ulam about magnetic fields generated by knotted wires (with A. Enciso). Ergodic Theor. & Dynam. Sys. 39, 2048-2070.
- Euler flows and singular geometric structures (with R. Cardona and E. Miranda). Phil. Trans. R. Soc. A 377, 20190034.
2018
- Minimal graphs with micro-oscillations (with A. Enciso and M.A. García-Ferrero). J. Differential Equations 265, 3339-3344.
- A problem of Berry and knotted zeros in the eigenfunctions of the harmonic oscillator (with A. Enciso and D. Hartley). J. Eur. Math. Soc. 20, 301-314.
- The Biot-Savart operator of a bounded domain (with A. Enciso and M.A. García-Ferrero). J. Math. Pures Appl. 119, 85-113.
- When do knots in light stay knotted? (with H. Kedia and W. Irvine). J. Phys. A: Math. Theor. 51, 025204.
- Topological aspects of critical points and level sets in elliptic PDEs (with A. Enciso). Lecture Notes in Mathematics 2220, 89-119.
- Dislocations of arbitrary topology in Coulomb eigenfunctions (with A. Enciso and D. Hartley). Rev. Mat. Iberoam. 34, 1361-1371.
2017
- Vortex reconnection in the three dimensional Navier-Stokes equations (with A. Enciso and R. Luca). Adv. Math. 309, 452-486.
- Knotted structures in high-energy Beltrami fields on the torus and the sphere (with A. Enciso and F. Torres de Lizaur). Ann. Sci. Éc. Norm. Sup. 50, 995-1016.
- Existence of minimal flows on nonorientable surfaces (with J.G. Espín and G. Soler). Discrete Cont. Dyn. Sys. 37, 4191-4211.
- Prescribing the nodal set of the first eigenfunction in each conformal class (with A. Enciso and S. Steinerberger). Int. Math. Res. Notices 2017, 3322-3349.
- Arnold diffusion of charged particles in ABC magnetic fields (with A. Luque). J. Nonlinear Sci. 27, 721-774.
2016
- Bounded solutions to the Allen-Cahn equation with level sets of any compact topology (with A. Enciso). Anal. & PDE 9, 1433-1446.
- Beltrami fields with a nonconstant proportionality factor are rare (with A. Enciso). Arch. Rat. Mech. Anal. 220, 243-260.
- Topological monsters in elliptic equations and spectral theory (with A. Enciso). EMS Surv. Math. Sci. 3, 107-130.
- Foliated vector fields without periodic orbits (with A. del Pino and F. Presas). Israel J. Math. 214, 443-462.
- Realization problems for limit cycles of planar polynomial vector fields (with J. Margalef-Bentabol). J. Differential Equations 260, 3844-3859.
- Laplace operators with eigenfunctions whose nodal set is a knot (with A. Enciso and D. Hartley). J. Funct. Anal. 271, 182-200.
- Stationary isothermic surfaces in Euclidean 3-space (with R. Magnanini and S. Sakaguchi). Math. Ann. 364, 97-124.
- Helicity is the only integral invariant of volume-preserving transformations (with A. Enciso and F. Torres de Lizaur). Proc. Natl. Acad. Sci. 113, 2035-2040.
2015
- Existence of knotted vortex tubes in steady Euler flows (with A. Enciso). Acta Math. 214, 61-134.
- Critical points and geometric properties of Green's functions on open surfaces (with A. Enciso). Ann. Mat. Pura Appl. 194, 881-901.
- Eigenfunctions with prescribed nodal sets (with A. Enciso). J. Differential Geom. 101, 197-211.
2014
- KAM theory and the 3D Euler equation (with B. Khesin and S. Kuksin ). Adv. Math. 267, 498-522.
2013
- Some geometric conjectures in harmonic function theory (with A. Enciso). Ann. Mat. Pura Appl. 192, 49-59.
- Submanifolds that are level sets of solutions to a second-order elliptic PDE (with A. Enciso). Adv. Math. 249, 204-249.
- Motion of charged particles in ABC magnetic fields (with A. Luque). SIAM J. Appl. Dyn. Syst. 12, 1889-1947.
- Tying knots in light fields (with H. Kedia, I. Byalinicki-Birula and W. Irvine). Phys. Rev. Lett. 111, 150404.
2012
- Critical points of Green's functions on complete manifolds (with A. Enciso). J. Differential Geom. 92, 1-29.
- A note on the first integrals of vector fields with integrating factors and normalizers (with J. Llibre). SIGMA 8, 035 (1-9).
- A note on the Liouvillian integrability and the qualitative properties of the mass rate equation for black holes (with J. Giné). J. Math. Phys. 53, 062701 (1-9).
- Integrable embeddings and foliations (with G. Hector). Amer. J. Math. 134, 773-825.
- Existence of inverse integrating factors and Lie symmetries for degenerate planar centers (with J. Giné). J. Differential Equations 252, 344-357.
- Knots and links in steady solutions of the Euler equation (with A. Enciso). Ann. of Math. 175, 345-367.
- Nondegeneracy of the eigenvalues of the Hodge Laplacian for generic metrics on 3-manifolds (with A. Enciso). Trans. Amer. Math. Soc. 364, 4207-4224.
2010
- Motion of charged particles in magnetic fields created by symmetric configurations of wires (with J. Aguirre and A. Luque). Phys. D 239, 654-675.
2009
- Symmetry for an overdetermined boundary problem in a punctured domain (with A. Enciso). Nonlinear Anal. 70, 1080-1086.
- Global attractors of analytic plane flows (with V. Jiménez-López). Ergodic Theor. & Dynam. Sys. 29, 967-981.
- Critical points and level sets in exterior boundary problems (with A. Enciso). Indiana Univ. Math. J. 58, 1947-1969.
- A symmetry result for the p-Laplacian in a punctured manifold (with A. Enciso). J. Math. Anal. Appl. 354, 619-624.
- A note on linear differential equations with periodic coefficients (with M. Grau). Nonlinear Anal. 71, 3197-3202.
- Existence and vanishing set of inverse integrating factors for analytic vector fields (with A. Enciso). Bull. London Math. Soc. 41, 1112-1124.
2008
- Integrability of magnetic fields created by current distributions (with J. Aguirre and J. Giné). Nonlinearity 21, 51-69.
- Period function and normalizers of vector fields in Rn with n-1 first integrals. J. Differential Equations 244, 1287-1303.
- Morse-type inequalities for dynamical systems and the Witten Laplacian (with A. Enciso). J. Differential Equations 244, 2804-2819.
2007
- Geometrical and topological aspects of electrostatics on Riemannian manifolds (with A. Enciso). J. Geom. Phys. 57, 1679-1696; ibid. 58 (2008) 1267-1269.
- Symmetric submersions of Rn to Rm (with A. Díaz-Cano and F.G. Gascón). Nonlinear Anal. 67, 2424-2432.
- Attractors and symmetries of vector fields: the inverse problem (with F.G. Gascón). J. Math. Anal. Appl. 335, 789-807.
- Realistic examples of chaotic magnetic fields created by wires (with J. Aguirre). Europhys. Lett. 80, 60007(1-6).
2006
- On scattering trajectories of dynamical systems (with A. Díaz-Cano and F.G. Gascón). J. Math. Phys. 47, 062703(1-10).
- Dynamic Parrondo's paradox (with J.S. Cánovas and A. Linero). Phys. D 218, 177-184.
- Note on the Markus-Yamabe conjecture for gradient dynamical systems (with F. Mañosas). J. Math. Anal. Appl. 322, 580-586; ibid 342 (2008) 1492.
- A geometric approach to the classification of the equilibrium shapes of self-gravitating fluids (with A. Pelayo). Comm. Math. Phys. 267, 93-115.
- The classical and quantum integrability of Hamiltonians without scattering states (with A. Enciso). Theor. Math. Phys. 148, 1086-1099.
2005
- Can two chaotic systems give rise to order? (with J. Almeida and M. Romera). Phys. D 200, 124-132.
- Some properties of the magnetic fields generated by symmetric configurations of wires (with F.G. Gascón). Phys. D 206, 109-120.
- Note on a paper by J. Llibre and G. Rodríguez concerning algebraic limit cycles. J. Differential Equations 217, 249-256.
- Bagpipes configurations in mechanics and electromagnetism (with F.G. Gascón). Math. Comput. Modelling 42, 921-930.
2004
- Unbounded trajectories of dynamical systems (with F.G. Gascón and A. Pelayo). Appl. Math. Lett. 17, 253-259.
- On the construction of global coordinate systems in Euclidean spaces (with F.G. Gascón). Nonlinear Anal. 57, 723-742.
- Invariant sets of second order differential equations (with F.G. Gascón). Phys. Lett. A 325, 340-354.
- Motion of a charge in the magnetic field created by wires: impossibility of reaching the wires (with F.G. Gascón). Phys. Lett. A 333, 72-78.
2003
- Escape to infinity under the action of a potential and a constant electromagnetic field (with F.G. Gascón). J. Phys. A 36, 6441-6455.
2001
- Dynamical systems embedded into Lie algebras (with F.G. Gascón and O.R. Campoamor-Stursberg). J. Math. Phys. 42, 5741-5752.
- Ordered behavior in force-free magnetic fields (with F.G. Gascón). Phys. Lett. A 292, 75-84.
2000
- Symmetries and first integrals of divergence-free R3 vector fields (with F.G. Gascón). Int. J. Nonlinear Mech. 35, 589-596.
- Escape to infinity in a Newtonian potential (with F.G. Gascón). J. Phys. A 33, 5361-5368.
- On the first integrals of Lotka-Volterra systems (with F.G. Gascón). Phys. Lett. A 266, 336-340.
- A separation bound for non-Hamiltonian differential equations with proper first integrals (with F.G. Gascón and J. Ruiz). J. Math. Phys.41, 2922-2930.
1999
- Limit velocity of charged particles in a constant electromagnetic field under friction (with F.G. Gascón and J.M. Vegas). Phys. Lett. A 251, 39-43.
- Instability of vector fields induced by first integrals (with F.G. Gascón). J. Math. Phys. 40, 3099-3103.
Contact data
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