Publications

2020

  • L. Arnaut and S. Ibañez, Self-sustained oscillations and global climate changes Scientific Reports, 10 (2020) .
  • P. G. Barrientos, S. Kiriki, Y. Nakano, A. Raibekas and T. Soma, Historic behavior in nonhyperbolic homoclinic classes Proc. Amer. Math. Soc., 3, 1195-1206 (2020)
  • R. Barrio, M. Martínez, L. Pérez, E. Pueyo, Bifurcations and slow-fast analysis in a cardiac cell model for investigation of early afterdepolarizations Mathematics, 8, 880-896 (2020)
  • P. Pérez, A. Ruiz-Herrera and A. M. San Luis, Management guidelines in disturbance-prone populations J. Theor. Biology, 486 (2020)
  • H. A. El-Morshedy and A. Ruiz-Herrera, Criteria of global attraction in systems of delay differential equations with mixed monotonicity J. Differential Equations, 268, 5945-5968 (2020)
  • J. San Martín, F. Drubi and D. Rodríguez Pérez, Uncritical polarized groups: the impact of spreading fake news as fact in social networks Math. Comput. Simulation, 178, 192-206 (2020)
  • R. Barrio, S. Ibañez, L. Pérez and S. Serrano, Spike-adding structure in fold/hom bursters Nonlinear Sci. Numer. Simul., 83 (2020)
  • R. Barrio, S. Ibañez and L. Pérez, Homoclinic organization in the Hindmarsh-Rose model: a three-parameter study Chaos, 30 (5) (2020)
  • I. Baldomá, S. Ibañez and T. M. Seara, Hopf-zero singularities truly unfold chaos Commun. Nonlinear Sci. Numer. Simul., 84 (2020)
  • F. Drubi, S. Ibañez and D.Rivela, Chaotic behaviour in the unfolding of Hopf.Bogdanov-Takens singularities Discrete and continuous dynamical systems – Series B, 25, 599-615 (2020)

2019

  • A. Ruiz-Herrera, Attraction to equilibria in stage-structured predator prey models and bio-control problems. J. Dynam. Differential Equations, 31, 435-450 (2019)
  • H. A. El-Morshedy and A. Ruiz-Herrera, Global convergence to equilibria in non-monotone delay differential equations. Proc. Amer. Math. Soc., 147, 2095-2105 (2019)
  • J. Mierczynsky, L. Niu and A. Ruiz-Herrera, Linearization and invariant manifolds on the carrying simplex for competitive maps. J. Differential Equations, 267, 7385-741 (2019)
  • P. S. Casas, M. Garzón, L. J. Gray and J. A. Sethian, Numerical study on electrohydrodynamic multiple droplet interactions. Phys. Rev. E, 100 (2019)
  • B. García, J. Llibre and A. Lombardero, An algorithm for providing the normal forms of spatial quasi-homogeneous polynomial differential systems. J. Symbolic Comput., 95, 1-25 (2019)
  • A. Pumariño, J. A. Rodríguez and E. Vigil, How to analytically prove the existence of strange attractors using measure theory. Nonlinear analysis and boundary value problems, Spriger Proc. Math. Stat., 292, 29-40 (2019)
  • P. G. Barrientos, A. Raibekas and A. Rodrigues, Chaos near a reversible bifocus. Dynamical Systems, 34, 504-516 (2019)
  • F. Drubi, S. Ibañez and D.Rivela, A formal classification of Hopf-Bogdanov-Takens singularities of codimension three. Journal of Mathematical Analysis and Applications, 480 (2019)
  • F. Drubi and A. Ruiz-Herrera, Understanding bacterial cheating: Biological and practical implications. SIAM Journal of Applied Dynamical Systems, 18, 2303-2324 (2019)
  • A. Pumariño, J. A. Rodríguez and E. Vigil, Persistent 2D strange attractors for a two-parameter familiy of Expanding Baker Maps. Discrete and Contin. Dyn. Syst. Ser. B, 24 (2), 657-670 (2019)

2018

  • B. Alarcón, S. B. S. D. Castro and I. Labouriau, Global saddles for planar maps. Journal of dynamics and differential equations, 30 (2), 601-612 (2018)
  • S. Ibáñez, A. Pumariño and J. A. Rodríguez, Complexity and dynamical uncertainty. Studies in Systems, Decision and Control, 142, 855-867 (2018)
  • A. Ruiz-Herrera and P. Torres, Effects of diffusion on total biomass in simple metacommunities. Journal of Theoretical Biology, 447, 12-24 (2018)
  • L. Niu and A. Ruiz-Herrera, Trivial dynamics in discrete-time-systems: carrying simplex and translation arcs. Nonlinearity, 31 (6), 2633-2650 (2018)
  • P. G. Barrientos and A. Raibekas, Robustly non-hyperbolic transitive symplectic dynamics. Discrete Contin. Dyn. Syst., 38, 5993-6013 (2018)
  • A. Ruiz-Herrera, Metapopulation dynamics and total biomass: Understanding the effects of diffusion in complex networks. Theoretical population biology, 121, 1-11 (2018)
  • B. García, A. Lombardero and J. S. Pérez del Rio, Classification and counting of planar quasi-homogeneous differential systems through their weight vectors. Qualitative Theory and Dynamical Systems, 17, 541-561 (2018)
  • A. Pumariño, J. A. Rodríguez and E. Vigil, Renormalization of two-dimensional piecewise linear maps: Abundance of 2-D strange attractors . Discrete and Continuous Dynamical Systems 38 (2), 941-966 (2018).
  • S. Ibáñez, A. Pumariño and J. A. Rodríguez, Complexity and Dynamical Uncertainty . The Mathematics of the Uncertain. Studies in Systems, Decision and Control, 142, Springer, 855-867 (2018).

2017

  • J. F. Alves, A. Pumariño and E. Vigil, Statistical stability for multidimensional piecewise expanding maps . Proceedings of the American Mathematical Society, 145 (7), 3057-3068 (2017).
  • A. Pumariño, J. A. Rodríguez and E. Vigil, Renormalizable Expanding Baker Maps: Coexistence of strange attractors . Discrete and Continuous Dynamical Systems 37 (3), 1651-1678 (2017).
  • R. Barrio, S. Ibáñez and L. Pérez, Hindmarsh-Rose model: Close and far to the singular limit . Physics Letters a, 381 (6), 597-603 (2017).

2016

  • P. G. Barrientos, S. Ibáñez and J. A. Rodríguez, Robust cycles unfolding from conservative bifocal homoclinic orbits . Dynamical Systems-an International Journal, 31 (4), 546-579 (2016).

2015

  • A. Pumariño, J. A. Rodríguez, J. C. Tatjer and E. Vigil, Chaotic dynamics for two-dimensional tent maps . Nonlinearity, 28 (2), 407-434 (2015).
  • S. Ibáñez and A. A. Rodrigues, On the Dynamics Near a Homoclinic Network to a Bifocus: Switching and Horseshoes . International Journal of Bifurcation and Chaos, 25 (11) (2015).
  • B. Alarcón, S.B.S.D. Castro, I. Labouriau., Discrete Symmetric Planar Dynamics , To appear in Mathematics of Planet Earth, CIM-MS, Springer (2015).
  • P. G. Barrientos and A. Raibekas, Dynamics of iterated function systems on the circle close to rotations . Ergodic Theory and Dynamical Systems, 35(5), 1345-1368 (2015) .
  • P. G. Barrientos A family of eventually expanding piecewise linear maps of the interval . The American Mathematical Monthly 122 (7), 674-680 (2015).

2014

  • A. Pumariño, J. A. Rodríguez, J. C. Tatjer and E. Vigil, Expanding Baker maps as models for the dynamics emerging from 3D-homoclinic bifurcations. Discrete Contin. Dyn. Syst. Ser. B 19 (2), 523–541 (2014).
  • B. García, J. Llibre and J. S. Pérez del Río, Limit cycles of generalized Liénard polynomial differential systems via averaging theory. Chaos Solitons Fractals 62/63, 1–9 (2014).
  • P. G. Barrientos, A. Fakhari and A. Sarizadeh, Density of fiberwise orbits in minimal iterated function systems on the circle. Discrete Contin. Dyn. Syst. 34 (9), 3341–3352 (2014).
  • P. G. Barrientos, Y. Ki and A. Raibekas, Symbolic blender-horseshoes and applications . Nonlinearity 27 (12), 2805-2839 (2014).

2013

  • B. Alarcón, Rotation numbers for planar attractors of equivariant homeomorphisms. Topol. Methods Nonlinear Anal. 42 (2), 327–343 (2013).
  • B. Alarcón, S. B. S. D Castro and I. S. Labouriau, Global dynamics for symmetric planar maps. Discrete Contin. Dyn. Syst. 33 (6), 2241–2251 (2013).
  • Progress and challenges in dynamical systems. Proceedings of the International Conference “Dynamical Systems: 100 Years after Poincaré” held in Gijón, September 3–7, 2012. Edited by S. Ibáñez, J. S. Pérez del Río, A. Pumariño and J. A. Rodríguez. Springer Proceedings in Mathematics & Statistics, 54. Springer, Heidelberg, xxvi+411 pp. ISBN: 978-3-642-38830-9 (2013).
  • F. Dumortier, S. Ibáñez, H. Kokubu and C. Simó, About the unfolding of a Hopf-zero singularity. Discrete Contin. Dyn. Syst. 33, (10), 4435–4471 (2013).
  • A. Pumariño, J. A. Rodríguez, J. C. Tatjer and E. Vigil, Piecewise linear bidimensional maps as models of return maps for 3D diffeomorphisms. Progress and challenges in dynamical systems. Springer Proc. Math. Stat., 54, Springer, 351–366 (2013).
  • B. García, J. Llibre and J. S. Pérez del Río, Planar quasi-homogeneous polynomial differential systems and their integrability. J. Differential Equations 255 (10), 3185–3204 (2013).

2012

  • B. Alarcón, S. B. S. D Castro and I. S. Labouriau, A local but not global attractor for a Zn-symmetric map. J. Singul. , 1–14 (2012).
  • B. Alarcón, S. B. S. D Castro and I. S. Labouriau, The discrete Markus-Yamabe problem for symmetric planar polynomial maps. Indag. Math. (N.S.) 23 (3), 603–608 (2012).
  • R. Labarca, C. Moreira, A. Pumariño and J. A. Rodríguez, On bifurcation sets for symbolic dynamics in the Milnor-Thurston world. Commun. Contemp. Math. 14 (4), 1250024, 16 pp (2012).
  • B. García, J. Giné, M. Grau and J. S. Pérez del Río, On the multiplicity of algebraic limit cycles. J. Dynam. Differential Equations 24 (3), 539–560 (2012).
  • B. García, J. Llibre and J. S. Pérez del Río, On the polynomial differential systems having polynomial first integrals. Bull. Sci. Math. 136 (3), 309–316 (2012).

2011

  • B. Alarcón, S. B. S. D Castro and I. S. Labouriau, A Zn-Symmetric local but not global attractor (2011).
  • P. G. Barrientos, S. Ibáñez and J. A. Rodríguez, Heteroclinic cycles arising in generic unfoldings of nilpotent singularities . Journal of Dynamics and Differential Equations (2011).
  • F. Drubi, S. Ibáñez and J. A. Rodríguez, Hopf-pitchfork singularities in coupled systems, Physica D: Nonlinear Phenomena . 240, 825-840 (2011).
  • B. García, H. Giacomini and J. S. Pérez del Río, Planar polynomial vector fields having a polynomial first integral can be obtained from linear systems . Applied Mathematics Letters, 24 (7), 1115-1119 (2011).

2009

  • B. García, J. Llibre and J. S. Pérez del Río, Corrigendum to ‘’On the number of limit cycles surrounding a unique singular point for polynomial differential systems of arbitrary degree’’ . Nonlinear Analysis, Theory, Methods and Applications, 71 (5-6), 2385-2386 (2009).
  • S. Ibáñez, A. Pumariño and J. A. Rodríguez, Sembrando el caos . Boletín de la Sociedad Española de Matemática Aplicada, 48, 59-84 (2009).
  • R. Labarca, A. Pumariño and J. A. Rodríguez, On the boundary of the topological chaos for the Milnor-Thurston world . Commun. Contemp. Math., 11 (6), 1049-1066 (2009).

2008

  • B. Alarcón, V. Guíñez and C. Gutierrez. Planar embeddings with a globally attracting fixed point. Nonlinear Analysis, 69, 140-150, 2008.
  • B. Alarcón, C. Gutierrez and J. Martínez-Alfaro, Planar maps whose second iterate has a unique fixed point. Journal of Difference Equations and Applications, 14, 421-428, 2008.
  • B. García, J. Llibre and J. S. Pérez del Río, On the number of limit cycles surrounding a unique singular point for polynomial differential systems of arbitrary degree . Nonlinear Anal., 69 (12), 4461-4469 (2008).
  • F. Drubi, S. Ibáñez and J. A. Rodríguez, Singularities and chaos in coupled systems . Bull. Belg. Math. Soc. Simon Stevin, 15 (5), 797-808 (2008).
  • C. Escudero and J. A. Rodríguez, Persistence of instanton connections in chemical reactions with time-dependent rates . Phys. Rev. E (3), 77 (1), 011130, 9 pp (2008).

2007

  • B. Alarcón, V. Guíñez and C. Gutierrez. Hopf bifurcation at infinity for planar vector fields. Discrete and Continuous Dynamical Systems. Series A, 17, 247-258, 2007.
  • F. Drubi, S. Ibáñez and J. A. Rodríguez, Coupling leads to chaos . J. Differential Equations, 239 (2), 371-385 (2007).

2006

  • J. Chavarriga, B. García, J. Llibre, J. S. Pérez del Río and J. A. Rodríguez, Polynomial first integrals of quadratic vector fields . J. Differential Equations, 230, 393-421 (2006).
  • F. Dumortier, S. Ibáñez and H. Kokubu, Cocoon bifurcation in three-dimensional reversible vector fields . Nonlinearity, 19, 305-328 (2006).
  • B. García, J. Llibre and J. S. Pérez del Río, Phase portraits of the quadratic vector fields with a polynomial first integral . Rend. Circ. Mat. Palermo (2), 55 (3), 420-440 (2006).
  • A. Pumariño and J. C. Tatjer, Dynamics near homoclinic bifurcations of three-dimensional dissipative diffeomorphisms . Nonlinearity, 19(12), 2833-2852 (2006).

2005

  • S. Ibáñez, Orbitas Shil’nikov y bifurcaciones cocoon en despliegues de singularidades . Revista del Seminario Iberoamericano de Matemáticas, 3 (III), 45-59 (2005).
  • S. Ibáñez and J. A. Rodríguez, Shil’nikov homoclinic orbits in the unfolding of a codimension-3 singularity . en “International Conference on Differential Equations (Equadiff 2003), World Scientific Publishing”, 975-977 (2005).
  • S. Ibáñez and J. A. Rodríguez, Sil’nikov configurations in any generic unfolding of the nilpotent singularity ofcodimension three on R4 . J. Differential Equations, 208, 147-175 (2005).
  • A. Pumariño and J. C. Tatjer, A possible new family of two dimensional strange attractors . International conference on differential equations (Equadiff 2003). Edited by F. Dumortier, H. Broer, J. Mawhin, A. Vanderbauwhede and S. Verduyn Lunel. World Scientific, Singapore, 434-439 (2005).
  • A. Pumariño and C. Valls, Instability in hamiltonian systems . Electronic journal of qualitative theory of differential equations. Monograph series, 1, 1.204 (2005).

1994-2004

  • A. Pumariño and C. Valls, On the double pendulum: An example of double resonant situations . Discrete and continuous dynamical systems, 11 (2/3), 413-448 (2004).
  • L. Alsedá, M. A. del Río and J. A. Rodríguez, Transitivity and dense periodicity for graph maps . Journal of difference equations and applications, 9 (6), 577-598 (2003).
  • L. Alsedá, M. A. del Río and J. A. Rodríguez, A survey on the relation between transitivity and dense periodicity for graph maps . Journal of difference equations and applications, 9 (3/4), 281-288 (2003).
  • J. Llibre, J. Paraños and J. A. Rodríguez, Periods for continuous self maps of the figure-eight space . Internat. J. Bifurc. Chaos Appl. Sci. Engrg., 13 (7), 1743-1754 (2003).
  • L. Alsedá, M. A. del Río and J. A. Rodríguez, Cofiniteness of the set of periods for totally transitive graph maps . Internat. J. Bifurc. Chaos Appl. Sci Engrg., 11 (3), 841-843 (2001).
  • F. Dumortier, S. Ibáñez and H. Kokubu, New aspects in the unfolding of the nilpotent singularity of codimension three . Dyn. Syst., 16 (1), 63-95 (2001).
  • J. Llibre, J. S. Pérez del Río and J. A. Rodríguez, Averaging analysis of a perturbated quadratic center . Nonlinear Anal. , 46, 45-51 (2001).
  • A. Pumariño and J. A. Rodríguez, Coexistence and persistence of infinitely many strange attractors . Ergod. Th.& Dynam. Sys., 21, 1511-1523 (2001).
  • J. Llibre, J. S. Pérez del Río and J. A. Rodríguez, Structural stability of planar semi-homogeneous polynomial vector fields. Applications to critical points and to infinity . Discrete Contin. Dynam. Systems, 6 (4), 809-828 (2000).
  • J. Llibre, J. S. Pérez del Río and J. A. Rodríguez, Phase portraits of a new class of integrable quadratic vector fields . Dynam. Contin. Discrete Impuls. Systems, 7 (4), 595-616 (2000).
  • L. Alsedá, M. A. del Río and J. A. Rodríguez, A splitting theorem for transitive maps . J. Math. Anal. Appl., 232 (2), 359-375 (1999).
  • L. Alsedá, M. A. del Río and J. A. Rodríguez, Cofiniteness of the set of periods for totally transitive tree maps . Internat. J. Bifurc. Chaos Appl. Sci. Engrg., 9 (9), 1877-1880 (1999).
  • F. Dumortier and S. Ibáñez, Codimension 4 singularities of reflectionally symmetric vector fields . Pub. Mat. UAB, 43, 501-533 (1999).
  • J. Llibre, J. Paraños and J. A. Rodríguez, Sets of periods for maps on connected graphs with zero Euler characteristic having all branching points fixed . J. Math. Anal. Appl., 239 (1), 85-100 (1999).
  • F. Dumortier and S. Ibáñez, Singularities of vector fields on R3 . Nonlinearity, 11, 1037-1047 (1998).
  • J. Llibre, J. Paraños and J. A. Rodríguez, Periods for transversal maps on compact manifolds with a given homology . Houston J. Math., 24 (3), 397-407 (1998).
  • L. Alsedá, J. Paraños and J. A. Rodríguez, The full periodicity kernel for a class of graph maps . Acta Math. Univ. Comenian, 66 (2), 313-320 (1997).
  • C. Bonatti, A. Pumariño and M. Viana, Lorenz attractors with arbitrary expanding dimension . C.R. Acad. Sci. Paris Sér. I Math., 325 (8), 883-888 (1997).
  • A. Pumariño and J. A. Rodríguez, Coexistence and Persistence of Strange Attractors . Lecture Notes in Mathematics, 1658, viii+195 (1997).
  • F. Dumortier and S. Ibáñez, Nilpotent singularities in generic 4-parameter families of 3-dimensional vector fields . J. Differential Equations , 127, 590-647 (1996)
  • J. Llibre, J. S. Pérez del Rio and J. A. Rodríguez, Structural Stability of Planar Homogeneous Polynomial Vector Fields: Applications to Critical Points and to Infinity . J. Differential Equations, 125 (2), 490-520 (1996).
  • S. Ibáñez and J. A. Rodríguez, Sil’nikov bifurcations in generic 4-unfoldings of a codimension-4 singularity . J. Differential Equations , 120 (2), 411-428 (1995).
  • J. Llibre, J. Paraños and J. A. Rodríguez, On the extensión of Sarkovskii’s Theorem for connected graphs with non-positive Euler characteristic . Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5, 1395-1405 (1995).
  • J. Llibre, J. Paraños and J. A. Rodríguez, The full periodicity kernel for sigma maps . J. Math. Anal. Appl., 183 (3), 639-651 (1994).