Publications

2023

  • J. A. Rodríguez, Emergence of Strange Attractors from Singularities. Regular and Chaotic Dynamics, 28 (4-5), 468-497 (2023)
  • P. G. Barrientos and J. D. Rojas, Typical coexistence of infinitely many strange attractors. Mathematische Zeitschrift, 303, 34-48 (2023)
  • R. Barrio, S. Ibáñez and L. Pérez, Geometry of bifurcation sets: Exploring the parameter space. Preprint (2023)
  • F. Drubi, A. Mayora-Cebollero, C. Mayora-Cebollero, S. Ibáñez, J. A. Jover-Galtier, A. Lozano, L. Pérez and R. Barrio, Connecting chaotic regions in the Coupled Brusselator System. Chaos, Solitons and Fractals, 169 (2023)
  • B. García, J. Llibre, J. S. Pérez del Río and S. Pérez-González, Limit Cycles of Polynomially Integrable Piecewise Differential Systems. Axioms, 12 (4), 342 (2023)
  • A. Marqués-Lobeiras, A. Pumariño, J. A. Rodríguez and E. Vigil, Strictly Invariant Sets for 2-D Tent Maps: 2-D Strange Attractors. Bull Braz Math Soc, New Series, 54 (10) (2023)
  • A. Marqués-Lobeiras, A. Pumariño, J. A. Rodríguez and E. Vigil, Splitting and coexistence of 2-D strange attractors in a general family of Expanding Baker Maps. Nonlinearity, 36 (8) (2023)

2022

  • P. G. Barrientos, Historic wandering domains near cycles. Nonlinearity, 35, 3191-3208 (2022)
  • P. G. Barrientos, L. J. Díaz, S. A. Pérez, Homoclinic tangencies leading to robust heterodimensional cycles. Mathematische Zeitschrift, 302, 519-558 (2022)
  • P. G. Barrientos, Y. Nakano, A. Raibekas and M. Roldan, Topological entropy and Hausdorff dimension of irregular sets for non-hyperbolic dynamical systems. Dynamical Systems – An International Journal, 37, 1-30 (2022)

2021

  • J. F. Alves and A. Pumariño, Entropy formula and continuity of entropy for piecewise expanding maps. Annales de l’Institut Henri Poincaré C, Analyse non linéaire, 38 (1), 91-108 (2021)
  • R. Barrio, S. Ibáñez, L. Pérez, y S. Serrano, Classification of fold/hom and fold/Hopf spike-adding phenomena. Chaos, 31 (4) (2021)
  • F. Drubi, S. Ibáñez and P. Pilarczyk, Nilpotent singularities and chaos: tritrophic food chains. Chaos, Solitons and Fractals, 142 (2021)
  • B. García, J. Llibre, A. Lombardero and J. S. Pérez del Río, Analytic integrability of quasi-homogeneous systems via the Yoshida method. J. Symbolic Comput, 104, 960-980 (2021)

2020

  • L. Arnaut and S. Ibañez, Self-sustained oscillations and global climate changes. Scientific Reports, 10 (2020)
  • P. G. Barrientos and A. Fakhari, Ergodicity of non-autonomous discrete systems with non-uniform expansion. Discrete and Continuous Dynamical Systems-Series B, 25, 1361-1382 (2020)
  • P. G. Barrientos, M. Fitzsimmons, F. H. Ghane, D. Malicet And A. Sarizadeh, Addendum and corrigendum to ‘On the chaos game of iterated function systems’. Topological Methods in Nonlinear Analysis, 55, 1-616 (2020)
  • P. G. Barrientos, S. Kiriki, Y. Nakano, A. Raibekas and T. Soma, Historic behavior in non-hyperbolic homoclinic classes. Proceedings of the American Mathematical Society, 148, 1195-1206 (2020)
  • P. G. Barrientos and B. Malicet, Extremal exponents of random products of conservative diffeomorphisms. Mathematische Zeitschrift, 296, 1185-1207 (2020).
  • P. G. Barrientos and A. Raibekas, Robust Degenerate Unfoldings of Cycles and Tangencies. Journal of Dynamics and Differential Equations, 33, 177-209 (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)
  • B. García, J. Llibre, A. Lombardero and J. S. Pérez del Río, An algorithm for providing the normal forms of spatial quasi-homogeneous polynomial differential systems. J. Symbolic Comput, 95, 1-25 (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

  • P. G. Barrientos, A. Raibekas and A. Rodrigues, Chaos near a reversible bifocus. Dynamical Systems, 34, 504-516 (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)
  • 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)
  • 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)
  • 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)
  • 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)
  • 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, Springer Proc. Math. Stat., 292, 29-40 (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)
  • A. Ruiz-Herrera, Attraction to equilibria in stage-structured predator prey models and bio-control problems. J. Dynam. Differential Equations, 31, 435-450 (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)
  • P. G. Barrientos and A. Raibekas, Robustly non-hyperbolic transitive symplectic dynamics. Discrete Contin. Dyn. Syst., 38, 5993-6013 (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)
  • 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)
  • L. Niu and A. Ruiz-Herrera, Trivial dynamics in discrete-time-systems: carrying simplex and translation arcs. Nonlinearity, 31 (6), 2633-2650 (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)
  • A. Ruiz-Herrera, Metapopulation dynamics and total biomass: Understanding the effects of diffusion in complex networks. Theoretical population biology, 121, 1-11 (2018)
  • A. Ruiz-Herrera and P. Torres, Effects of diffusion on total biomass in simple metacommunities. Journal of Theoretical Biology, 447, 12-24 (2018)

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)
  • 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)

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

  • B. Alarcón, S.B.S.D. Castro, I. Labouriau, Discrete Symmetric Planar Dynamics. Dynamics, Games and Science, 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)
  • 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)
  • A. Pumariño, J. A. Rodríguez, J. C. Tatjer and E. Vigil, Chaotic dynamics for two-dimensional tent maps. Nonlinearity, 28 (2), 407-434 (2015)

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)
  • 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)
  • 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)

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)
  • 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)
  • 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)
  • 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)
  • 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)

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)
  • 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)
  • 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 (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. Gutiérrez, 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. Gutiérrez, 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. International conference on differential equations (Equadiff 2003). Edited by F. Dumortier, H. Broer, J. Mawhin, A. Vanderbauwhede and S. Verduyn Lunel. World Scientific, Singapore, 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)

    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)

    2003

    • 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)

    2001

    • 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. Theory Dyn. Syst., 21, 1511-1523 (2001)

    2000

    • 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)

    1999

    • 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)

    1998

    • 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)

    1997

    • 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)

    1996

    • 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)

    1995

    • 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)

    1994

    • J. Llibre, J. Paraños and J. A. Rodríguez, The full periodicity kernel for sigma maps. J. Math. Anal. Appl., 183 (3), 639-651 (1994)

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