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Research and publications

List of publications

  1. H. Barge, J.M.R. Sanjurjo, Shape index, Brouwer degree and Poincaré-Hopf theorem, arXiv:2303.06472
  2. H. Barge, L. Hernández-Corbato, On the growth rate inequality for self-maps of the sphere, arXiv:2301.08543
  3. H. Barge, J.J. Sánchez-Gabites, Knotted toroidal sets, attractors and incompressible surfaces, arXiv:2212.14642.
  4. H. Barge, J.J. Sánchez-Gabites, The realization problem of non-connected compacta as attractors, to appear in Top. Appl.
  5. H. Barge, J.M.R. Sanjurjo, The topology of dissipative systems, To appear in the Proceedings of the 8ECM.
  6. H. Barge, J.J. Sánchez-Gabites, The geometric index and attractors of homeomorphisms of R^3, Ergod. Th. & Dynam. Sys. 43 (2023), 50-77.
  7. H. Barge, J.M.R. Sanjurjo, Higher dimensional topology and generalized Hopf bifurcations for discrete dynamical systems, Discrete Contin. Dyn. Syst. 42 (2022), no. 6, 2585-2601.
  8. H. Barge, J.J. Sánchez-Gabites, Knots and solenoids that cannot be attractors of self-homeomorphisms of R^3, Int. Math. Res. Not. IMRN 2021, no. 13, 10373-10407.
  9. H. Barge, Cech cohomology, homoclinic trajectories and robustness of non-saddle sets, Discrete Contin. Dyn. Syst. 41 (2021), no. 6, 2677-2698.
  10. H. Barge, A. Giraldo, J.M.R. Sanjurjo, Bifurcations, robustness and shape of attractors of discrete dynamical systems, J. Fixed Point Theory Appl. 22 (2020), no. 2, Paper No. 29, 13 pp.
  11. H. Barge, J.M.R. Sanjurjo, Dissonant points and the region of influence of non-saddle sets, J. Differential Equations 268 (2020), no. 9, 5329-5352.
  12. H. Barge, J.M.R. Sanjurjo, A Conley index study of the evolution of the Lorenz strange set, Phys. D 401 (2020), 132162, 11 pp.
  13. H. Barge, J.M.R. Sanjurjo, Dissipative flows, global attractors and shape theory, Topology Appl. 258 (2019), 392-401.
  14. H. Barge, J.M.R. Sanjurjo, Flows in R^2_+ without interior fixed points, global attractors and bifurcations, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 112 (2018), no. 3, 671-683.
  15. H. Barge, J.M.R. Sanjurjo, Bifurcations and attractor-repeller splittings of non-saddle sets, J. Dynam. Differential Equations 30 (2018), no.1, 257-272.
  16. H. Barge, K. Wójcik, Mayer-Vietoris property of the fixed point index, Topol. Methods Nonlinear Anal. 50 (2017), no.2, 643-667.
  17. H. Barge, Regular blocks and Conley index of isolated invariant continua in surfaces, Nonlinear Anal. 146 (2016), 100-119.
  18. H. Barge, J.M.R. Sanjurjo, Fixed points, bounded orbits and attractors of planar flows, A mathematical tribute to Professor José María Montesinos Amilibia, 125-132, Dep. Geom. Topol. Fac. Cien. Mat. UCM, Madrid, 2016.
  19. H. Barge, J.M.R. Sanjurjo, Unstable manifold, Conley index and fixed points of flows, J. Math. Anal. Appl. 420 (2014), no.1, 835-851.

Books

  1. H. Barge Yáñez, A. Zamora Saiz, Topología, Sanz y Torres (2021).
  2. A. Zamora Saiz, H. Barge Yáñez, Geometría Afín y Proyectiva, Sanz y Torres (2022).
  3. H. Barge Yáñez, J. Martínez Mateo, J. Sánchez Hernández, J. Rojo Carulli, Álgebra Lineal, Fundación General de la U.P.M. (2020).