Algaba-Durán, Antonio;Fuentes-Díaz, Natalia;Gamero-Gutiérrez, Estanislao;García-García, Cristóbal:
On the integrability problem for the Hopf-zero singularity and its relation with the inverse Jacobi multiplier. Applied Mathematics and Computation. 2021. Vol: 405. Núm: 126241. https://doi.org/10.1016/j.amc.2021.126241.
Algaba-Durán, Antonio;Checa-Camacho, Isabel;Gamero-Gutiérrez, Estanislao;García-García, Cristóbal:
Characterizing Orbital-Reversibility Through Normal Forms. Qualitative Theory of Dynamical Systems. 2021. Vol: 20. Núm: 38. https://doi.org/10.1007/s12346-021-00478-6.
Algaba-Durán, Antonio;Gamero-Gutiérrez, Estanislao;García-García, Cristóbal:
Orbital Hypernormal Forms. Symmetry. 2021. Vol: 13. Núm: 1500. Pág. 1-28. https://doi.org/10.3390/sym13081500.
Algaba-Durán, Antonio;Fuentes-Díaz, Natalia;Gamero-Gutiérrez, Estanislao;García-García, Cristóbal:
Orbital normal forms for a class of three-dimensional systems with an application to Hopf-zero bifurcation analysis of Fitzhugh-Nagumo system. Applied Mathematics and Computation. 2020. Vol: 369. Pág. -----. 10.1016/j.amc.2019.124893.
Algaba-Durán, Antonio;Freire-Macias, Emilio;Gamero-Gutiérrez, Estanislao;García-García, Cristóbal:
New aspects of the orbital normal form of the Hopf singularity: The Rayleigh and the van der Pol forms. International Journal of Non-Linear Mechanics. 2018. Vol: 105. Núm: --. Pág. 20-26. 10.1016/j.ijnonlinmec.2018.07.010.
Algaba-Durán, Antonio;Fuentes-Díaz, Natalia;Gamero-Gutiérrez, Estanislao;García-García, Cristóbal:
Structural stability of planar quasi-homogeneous vector fields. Journal of Mathematical Analysis and Applications. 2018. Vol: 468. Núm: --. Pág. 212-226. https://doi.org/10.1016/j.jmaa.2018.08.005.
Algaba-Durán, Antonio;Freire-Macias, Emilio;Gamero-Gutiérrez, Estanislao;García-García, Cristóbal:
A bifurcation analysis of planar nilpotent reversible systems. Nonlinear Dynamics. 2017. Vol: 87. Pág. 835-849. 10.1007/s11071-016-3082-9.
Algaba-Durán, Antonio;Gamero-Gutiérrez, Estanislao;García-García, Cristóbal:
The center problem. A view from the normal form theory. Journal of Mathematical Analysis and Applications. 2016. Vol: 434. Núm: 1. Pág. 680-697. 10.1016/j.jmaa.2015.09.027.
Algaba-Durán, Antonio;Gamero-Gutiérrez, Estanislao;Merino-Morlesín, Manuel;Rodríguez-Luis, Alejandro José:
Resonances of periodic orbits in the Lorenz system. Nonlinear Dynamics. 2016. Vol: 84. Núm: 4. Pág. 2111-2136. 10.1007/s11071-016-2632-5.
Algaba-Durán, Antonio;Freire-Macias, Emilio;Gamero-Gutiérrez, Estanislao;Rodríguez-Luis, Alejandro José:
An exact homoclinic orbit and its connection with the Rossler system. Physics Letters A. 2015. Vol: 379. Núm: 16-17. Pág. 1114-1121. http://dx.doi.org/10.1016/j.physleta.2015.02.017.
Algaba-Durán, Antonio;Checa-Camacho, Isabel;García-García, Cristóbal;Gamero-Gutiérrez, Estanislao:
On orbital-reversibility for a class of planar dynamical systems. Communications in Nonlinear Science & Numerical Simulation. 2015. Vol: 20. Núm: 1. Pág. 229-239. 10.1016/j.cnsns.2014.05.007.
Algaba-Durán, Antonio;Gamero-Gutiérrez, Estanislao;García-García, Cristóbal:
THE REVERSIBILITY PROBLEM FOR QUASI-HOMOGENEOUS DYNAMICAL SYSTEMS. Discrete and Continuous Dynamical Systems. Series A. 2013. Vol: 33. Núm: 8. Pág. 3225-3236. 10.3934/dcds.2013.33.xx.
Algaba-Durán, Antonio;Freire-Macias, Emilio;Gamero-Gutiérrez, Estanislao;García-García, Cristóbal:
MONODROMY, CENTER--FOCUS AND INTEGRABILITY PROBLEMS FOR QUASI-HOMOGENEOUS POLYNOMIAL SYSTEMS. Nonlinear Analysis, Theory, Methods and Applications. 2010. Vol: 72. Núm: 3-4. Pág. 1726-1736.
Algaba-Durán, Antonio;Gamero-Gutiérrez, Estanislao;García-García, Cristóbal:
THE INTEGRABILITY PROBLEM FOR A CLASS OF PLANAR SYSTEMS. Nonlinearity. 2009. Vol: 22. Núm: 2. Pág. 395-420.
Algaba-Durán, Antonio;Freire-Macias, Emilio;Gamero-Gutiérrez, Estanislao;Rodríguez-Luis, Alejandro José:
RESONANCES OF PERIODIC ORBITS IN RO?SSLER SYSTEM IN PRESENCE OF A TRIPLE-ZERO BIFURCATION. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. 2007. Vol: 17. Núm: 6. Pág. 1997-2008.
Algaba-Durán, Antonio;Gamero-Gutiérrez, Estanislao;García-García, Cristóbal;Merino-Morlesín, Manuel:
A DEGENERATE HOPF-SADDLE-NODE BIFURCATION ANALYSIS IN A FAMILY OF ELECTRONIC CIRCUITS. Nonlinear Dynamics. 2007. Vol: 48. Núm: 1-2. Pág. 55-76.
Algaba-Durán, Antonio;Gamero-Gutiérrez, Estanislao;Rodríguez-Luis, Alejandro José:
A BIFURCATION ANALYSIS OF A SIMPLE ELECTRONIC CIRCUIT. Communications in Nonlinear Science & Numerical Simulation. 2005. Vol: 10. Núm: 2. Pág. 169-178.
Algaba-Durán, Antonio;Freire-Macias, Emilio;Gamero-Gutiérrez, Estanislao;García-García, Cristóbal:
AN ALGORITHM FOR COMPUTING QUASI-HOMOGENEOUS FORMAL NORMAL FORMS UNDER EQUIVALENCE. Acta Applicandae Mathematicae. 2004. Vol: 80. Núm: 3. Pág. 335-359.
Algaba-Durán, Antonio;Freire-Macias, Emilio;Gamero-Gutiérrez, Estanislao;García-García, Cristóbal:
QUASI-HOMOGENEOUS NORMAL FORMS FOR NULL LINEAR PART. Dynamics of Continuous, Discrete and Impulsive Systems. Series A: Mathematical Analysis. 2003. Vol: 10. Núm: 1-3. Pág. 247-261.
Algaba-Durán, Antonio;Merino-Morlesín, Manuel;Freire-Macias, Emilio;Gamero-Gutiérrez, Estanislao;Rodríguez-Luis, Alejandro José:
SOME RESULTS ON CHUA'S EQUATION NEAR A TRIPLE-ZERO LINEAR DEGENERACY. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. 2003. Vol: 13. Núm: 3. Pág. 583-608.
Algaba-Durán, Antonio;Freire-Macias, Emilio;Gamero-Gutiérrez, Estanislao;García-García, Cristóbal:
QUASI-HOMOGENEOUS NORMAL FORMS. Journal of Computational and Applied Mathematics. 2003. Vol: 150. Núm: 1. Pág. 193-216.
Algaba-Durán, Antonio;Fernandez-Sanchez, Fernando;Freire-Macias, Emilio;Gamero-Gutiérrez, Estanislao;Rodríguez-Luis, Alejandro José:
OSCILLATION-SLIDING IN A MODIFIED VAN DER POL-DUFFING ELECTRONIC OSCILLATOR. Journal of Sound and Vibration. 2002. Vol: 249. Núm: 5. Pág. 899-907.
Algaba-Durán, Antonio;Freire-Macias, Emilio;Gamero-Gutiérrez, Estanislao:
COMPUTING SIMPLEST NORMAL FORMS FOR THE TAKENS-BOGDANOV SINGULARITY. Qualitative Theory of Dynamical Systems. 2002. Vol: 3. Pág. 377-435.
Doedel-, Eusebius;Freire-Macias, Emilio;Gamero-Gutiérrez, Estanislao;Rodríguez-Luis, Alejandro José:
AN ANALYTICAL AND NUMERICAL STUDY OF A MODIFIED VAN DER POL OSCILLATOR. Journal of Sound and Vibration. 2002. Vol: 256. Núm: 4. Pág. 755-771.
Freire-Macias, Emilio;Gamero-Gutiérrez, Estanislao;Rodríguez-Luis, Alejandro José;Algaba-Durán, Antonio:
A NOTE ON THE TRIPLE-ZERO LINEAR DEGENERACY: NORMAL FORMS, DYNAMICAL AND BIFURCATION BEHAVIORS OF AN UNFOLDING. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. 2002. Vol: 12. Núm: 12. Pág. 2799-2820.
Algaba-Durán, Antonio;Freire-Macias, Emilio;Gamero-Gutiérrez, Estanislao:
CHARACTERIZING AND COMPUTING NORMAL FORMS USING LIE TRANSFORMS: A SURVEY. Dynamics of Continuous, Discrete and Impulsive Systems. Series A: Mathematical Analysis. 2001. Vol: 8. Núm: 4. Pág. 449-475.
Gamero-Gutiérrez, Estanislao:
ON THE NORMAL FORM OF THE TRIPLE-ZERO DEGENERACY WITH GEOMETRIC MULTIPLICITY TWO. Dynamics of Continuous, Discrete and Impulsive Systems. Series A: Mathematical Analysis. 2001. Vol: 8. Núm: 4. Pág. 531-550.
Algaba-Durán, Antonio;Merino-Morlesín, Manuel;Freire-Macias, Emilio;Gamero-Gutiérrez, Estanislao;Rodríguez-Luis, Alejandro José:
ON THE HOPF-PITCHFORK BIFURCATION IN THE CHUA'S EQUATION. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. 2000. Vol: 10. Núm: 2. Pág. 291-305.
Algaba-Durán, Antonio;Freire-Macias, Emilio;Gamero-Gutiérrez, Estanislao:
ISOCHRONICITY VIA NORMAL FORM. Qualitative Theory of Dynamical Systems. 2000. Vol: 1. Núm: 2. Pág. 133-156.
Algaba-Durán, Antonio;Freire-Macias, Emilio;Gamero-Gutiérrez, Estanislao;Rodríguez-Luis, Alejandro José:
A TAME DEGENERATE HOPF-PITCHFORK BIFURCATION IN A MODIFIED VAN DER POL-DUFFING OSCILLATOR. Nonlinear Dynamics. 2000. Vol: 22. Núm: 3. Pág. 249-269.
Freire-Macias, Emilio;Gamero-Gutiérrez, Estanislao;Rodríguez-Luis, Alejandro José:
FIRST-ORDER APPROXIMATION FOR CANARD PERIODIC ORBITS IN A VAN DER POL ELECTRONIC OSCILLATOR. Applied Mathematics Letters. 1999. Vol: 12. Núm: 2. Pág. 73-78.
Gamero-Gutiérrez, Estanislao;Freire-Macias, Emilio;Rodríguez-Luis, Alejandro José;Ponce-Nuñez, Enrique;Algaba-Durán, Antonio:
HYPERNORMAL FORM CALCULATION FOR TRIPLE-ZERO DEGENERACIES. Bulletin of the Belgian Mathematical Society Simon Stevin. 1999. Vol: 6. Núm: 3. Pág. 357-368.
Algaba-Durán, Antonio;Freire-Macias, Emilio;Gamero-Gutiérrez, Estanislao:
HYPERNORMAL FORMS FOR EQUILIBRIA OF VECTOR FIELDS. CODIMENSION ONE LINEAR DEGENERACIES. Rocky Mountain Journal of Mathematics. 1999. Vol: 29. Núm: 1. Pág. 13-45.
Algaba-Durán, Antonio;Freire-Macias, Emilio;Gamero-Gutiérrez, Estanislao;Rodríguez-Luis, Alejandro José:
ON A CODIMENSION-THREE UNFOLDING OF THE INTERACTION OF DEGENERATE HOPF AND PITCHFORK BIFURCATIONS. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. 1999. Vol: 9. Núm: 7. Pág. 1333-1362.
Algaba-Durán, Antonio;Freire-Macias, Emilio;Gamero-Gutiérrez, Estanislao;Rodríguez-Luis, Alejandro José:
A THREE-PARAMETER STUDY OF A DEGENERATE CASE OF THE HOPF- PITCHFORK BIFURCATION. Nonlinearity. 1999. Vol: 12. Núm: 4. Pág. 1177-1206.
Algaba-Durán, Antonio;Freire-Macias, Emilio;Gamero-Gutiérrez, Estanislao;Rodríguez-Luis, Alejandro José:
ON THE TAKENS-BOGDANOV BIFURCATION IN THE CHUA'S EQUATION. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences. 1999. Vol: E82-A. Núm: 9. Pág. 1722-1728.
Algaba-Durán, Antonio;Freire-Macias, Emilio;Gamero-Gutiérrez, Estanislao:
HYPERNORMAL FORM FOR THE HOPF-ZERO BIFURCATION. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. 1998. Vol: 8. Núm: 10. Pág. 1857-1887.
Gamero-Gutiérrez, Estanislao;Rodríguez-Luis, Alejandro José;Freire-Macias, Emilio:
STUDY OF A DEGENERATE BOGDANOV-TAKENS BIFURCATION IN A FAMILY OF MECHANICAL OSCILLATORS. Mechanics Research Communications. 1998. Vol: 25. Núm: 3. Pág. 287-297.
Algaba-Durán, Antonio;Freire-Macias, Emilio;Gamero-Gutiérrez, Estanislao;Rodríguez-Luis, Alejandro José:
ANALYSIS OF HOPF AND TAKENS-BOGDANOV BIFURCATIONS IN A MODIFIED VAN DER POL-DUFFING OSCILLATOR. Nonlinear Dynamics. 1998. Vol: 16. Núm: 4. Pág. 369-404.
Freire-Macias, Emilio;Rodríguez-Luis, Alejandro José;Gamero-Gutiérrez, Estanislao;Ponce-Nuñez, Enrique:
A CASE-STUDY FOR HOMOCLINIC CHAOS IN AN AUTONOMOUS ELECTRONIC-CIRCUIT - A TRIP FROM TAKENS-BOGDANOV TO HOPF-SILNIKOV. Physica D: Nonlinear Phenomena. 1993. Vol: 62. Núm: 1-4. Pág. 230-253.
Freire-Macias, Emilio;Gamero-Gutiérrez, Estanislao:
AN ALGORITHM FOR SYMBOLIC COMPUTATION OF CENTER MANIFOLDS. Lecture Notes in Computer Science. 1989. Vol: 358. Pág. 218-230.