List of  papers (from 2001).




Dynamical systems. Fixed point theory.


1)Lefschetz index of arbitrary planar homeomorphisms at isolated invariant continua  (with J. M. Salazar, preprint.)


2) Estimating basins of attraction (with L. Hernández-Corbato, preprint).


3) Stable sets of planar homeomorphism with translation pseudo-arcs (DCDS-S. (2017) accepted)


4) Uniqueness of dynamical zeta functions and symmetric products (with E. Blanco, J. Hernández-Corbato, J. Fixed Point Theory Appl. (2016).  )


5) Index 1 fixed points of orientation reversing planar homeomorphisms (with J.M. Salazar)(Topological Methods in Nonlinear Analysis, 2015)


6) Fixed point indices of continuous planar maps (with Luis Hernández-Corbato) (Discrete and Continuous Dynamical Systems A, 35 (2015) 2979 – 2995.


7) Cech cohomology of attractors of discrete dynamical systems (with J.J. Sánchez-Gabites)(Journal of Diff. Equations,  257 (2014) 2826-2845.)


8) About the homological discrete Conley index of isolated invariant acyclic continua (with L. Hernández-Corbato and P. Le Calvez)(Geometry & Topology 17, 5 (2013) 2977-3026).


9) Attractors with irrational rotation number (with L. Hernández-Corbato and R. Ortega) (Math. Proc. Cambridge Phil. Soc. 153, No 1 (2012) 59-77).


10) Attractors with vanishing rotation number (with R. Ortega) (Journal European Math. Soc.  13 (2011) 1567-1588).


11) Local fixed point indices of iterations of planar maps (with G. Graff and P. Nowak-Przygodzki).  (J. Dynamics and Diff. Equations, 23 (2011) 213-223).


12) Pointed shape and global attractors for metrizable spaces (with A. Giraldo, R. Jiménez, M.A. Morón and J.M.R. Sanjurjo). (Topology and its Appl.  158, (2011) 167-176).


13) Fixed point indices of the iterates of R3-homeomorphisms at fixed points which are isolated invariant sets  (with P.  Le Calvez and J. M. Salazar) (Journal of the London Math. Soc.  82 (2) (2010) 683-696).


14) Realization of all Dold’s congruences with stability (with J.M Salazar) (Journal of Differential Equations, 249 (2010) 989-1013).


15) A Poincaré formula for the fixed point indices of the iterations of planar homeomorphisms (with J.M. Salazar)

(Fixed Point Theory and its Appl. ID233069 (2010) 1-31).


16) Indices of the iterates of R3-homeomorphisms at Lyapunov stable fixed points (with J.M. Salazar)

(Journal of Differential Equations, 244, 5 (2008) 1141-1156).


17) A note about the shape of attractors of discrete semidynamical systems (with M.A. Morón)

(Proceedings of the American Mathematical Society, 134 (2006) 2165-2167). 


18) A stable/unstable manifold theorem for local homeomorphisms of the plane (with J.M. Salazar)

(Ergodic Theory and Dynamical Systems, 25 (2005) 301-317).


19) Shape of global attractors in topological spaces (with A. Giraldo, M.A. Morón and J.M.R. Sanjurjo)

(Nonlinear Analysis. Theory, Methods and Appl. 60 (2005) 837-847).


20) Planar isolated and stable fixed points have index =1

(Journal of Differential Equations, 199, 1 (2004) 179-188).


21) Fixed point index and decompositions of planar invariant compacta (with J.M. Salazar)

(Topology and its Applications, 141 (2004) 207-223).


22) Generalized Complementing maps

(Contribuciones Matemáticas. Editorial UCM. (2004)).


23) Shape index in metric spaces (with J.M. Salazar)

(Fundamenta Mathematicae, 176 (2003) 1, 47-62).


24) Fixed point index of iterations of local homeomorphisms of the plane: a Conley index approach (with J.M. Salazar)

(Topology, 41, 6 (2002), 1199-1212).


25) Fixed point index in hyperspaces: A Conley-type index for discrete semidynamical systems (with J.M. Salazar)

(Journal of the London Mathematical Society, 64, 1 (2001) 191-204).


26) Some duality properties of non-saddle sets (with A. Giraldo, M.A. Morón and J.M.R. Sanjurjo)

(Topology and its Applications, 113 (2001) 51-59).




Geometric Topology. Shape Theory.



1) Ultrametric spaces, valued and semivalued groups arising from the Theory of Shape (with E. Cuchillo-Ibáñez and M.A. Morón) Libro Homenaje al professor Joan Tarrés (2012).


2) Monomorphisms and epimorphims in pro-categories (with J. Dydak)

(Topology and its Applications, 154, 10 (2007) 2204-2222).


3) Isomorphisms in pro-categories (with J.Dydak)

(Journal of Pure and Applied Algebra, 190 (2004) 85-120).


4) Finite approximations to Cech homology (with A. Giraldo, M.A. Morón and  J.M.R. Sanjurjo)

(Journal of Pure and Applied Algebra, 163, 1 (2001) 81-92).














Tesis doctorales dirigidas.



- José Manuel Salazar. Indice de punto fijo en hiperespacios e índice de Conley. (Premio extraordinario de Doctorado, 2001).


-Luis Hernández Corbato. On the dynamics of homeomorphisms around fixed points in low dimension.