|
[1]
|
A. Algaba, I. Checa, C. García and J. Giné, Analytic integrability inside a family of degenerate centers, Nonlinear Anal. Real World Appl., 31 (2016), 288-307.
doi: 10.1016/j.nonrwa.2016.02.003.
|
|
[2]
|
A. Algaba, E. Freire, E. Gamero and C. García, Quasi-homogeneous normal forms, J. Comput. Appl. Math., 150 (2003), 193-216.
doi: 10.1016/S0377-0427(02)00660-X.
|
|
[3]
|
A. Algaba, E. Freire, E. Gamero and C. García, An Algorithm for computing quasi-homogeneous formal normal forms under equivalence, Acta Appl. Math., 80 (2004), 335-339.
doi: 10.1023/B:ACAP.0000018769.73927.a4.
|
|
[4]
|
Monodromy, center-focus and integrability problems for quasi-homogeneous polynomial systems, Nonlinear Analysis, 72 (2010), 1726–1736.
doi: 10.1016/j.na.2009.09.012.
|
|
[5]
|
A. Algaba, E. Gamero and C. García, The integrability problem for a class of planar systems, Nonlinearity, 22 (2009), 395-420.
doi: 10.1088/0951-7715/22/2/009.
|
|
[6]
|
A. Algaba, C. García and J. Giné, Analytic integrability for some degenerate planar systems, Commun. Pure Appl. Anal., 12 (2013), 2797-2809.
doi: 10.3934/cpaa.2013.12.2797.
|
|
[7]
|
A. Algaba, C. García and J. Giné, Analytic integrability for some degenerate planar vector fields, J. Differential Equations, 257 (2014), 549-565.
doi: 10.1016/j.jde.2014.04.010.
|
|
[8]
|
A. Algaba, C. García and J. Giné, Analytic integrability of some examples of degenerate planar vector fields, Acta Appl. Math., 141 (2016), 1-15.
doi: 10.1007/s10440-014-0001-2.
|
|
[9]
|
A. Algaba, C. García and J. Giné, Analytic integrability around a nilpotent singularity, J. Differential Equations, 267 (2019), 443-467.
doi: 10.1016/j.jde.2019.01.015.
|
|
[10]
|
A. Algaba, C. García and J. Giné, Integrability of planar nilpotent differential systems through the existence of an inverse integrating factor, Commun. Nonlinear Sci. Numer. Simul., 71 (2019), 130-140.
doi: 10.1016/j.cnsns.2018.09.018.
|
|
[11]
|
A. Algaba, C. García and M. Reyes, Like-linearization of vector fields, Bull. Sci. Math., 133 (2009), 806-816.
doi: 10.1016/j.bulsci.2009.09.006.
|
|
[12]
|
A. Algaba, C. García and M. Reyes, Integrability of two dimensional quasi-homogeneous polynomial differential systems, Rocky Mountain J. Math., 41 (2011), 1-22.
doi: 10.1216/RMJ-2011-41-1-1.
|
|
[13]
|
A. Algaba, C. García and M. Reyes, Existence of an inverse integrating factor, center problem and integrability of a class of nilpotent systems, Chaos Solitons Fractals, 45 (2012), 869-878.
doi: 10.1016/j.chaos.2012.02.016.
|
|
[14]
|
A. Baider and J. A. Sanders, Further reduction of the Takens-Bogdanov normal form, J. Differential Equations, 99 (1992), 205-244.
doi: 10.1016/0022-0396(92)90022-F.
|
|
[15]
|
C. B. Collins, Algebraic conditions for a centre or a focus in some simple systems of arbitrary degree, J. Math Anal. Appl., 195 (1995), 719-735.
doi: 10.1006/jmaa.1995.1385.
|
|
[16]
|
J. Chavarriga, H. Giacomini, J. Giné and J. Llibre, On the integrability of two-dimensional flows, J. Differential Equations, 157 (1999), 163-182.
doi: 10.1006/jdeq.1998.3621.
|
|
[17]
|
J. Chavarriga, H. Giacomini, J. Giné and J. Llibre, Local analytic integrability for nilpotent centers, Ergodic Theory Dynam. Systems, 23 (2003), 417-428.
doi: 10.1017/S014338570200127X.
|
|
[18]
|
A. Ferragut, J. Llibre and A. Mahdi, Polynomial inverse integrating factors for polynomial vector fields, Discrete Contin. Dyn. Syst., 17 (2006), 387-395.
doi: 10.3934/dcds.2007.17.387.
|
|
[19]
|
J. Giné, Analytic integrability and characterization of centers for nilpotent singular points, Z. Angew. Math. Phys., 55 (2004), 725-740.
doi: 10.1007/s00033-004-1093-8.
|
|
[20]
|
J. Giné, Analytic integrability and characterization of center for generalized nilpotent singular points, Appl. Math. Comput., 148 (2004), 849-868.
doi: 10.1016/S0096-3003(02)00941-4.
|
|
[21]
|
J. Giné, Reduction of integrable planar polynomial differential systems, Appl. Math. Lett., 25 (2012), 1862-1865.
doi: 10.1016/j.aml.2012.02.047.
|
|
[22]
|
J. Giné, M. Grau and J. Llibre, Polynomial and rational first integrals for planar quasi-homogeneous polynomial differential systems, Discrete Contin. Dyn. Syst., 33 (2013), 4531-4547.
doi: 10.3934/dcds.2013.33.4531.
|
|
[23]
|
A. Goriely, Integrability, partial integrability, and nonintegrability for systems of ordinary differential equations, J. Math. Phys., 37 (1996), 1871-1893.
doi: 10.1063/1.531484.
|
|
[24]
|
M. Han and K. Jiang, Normal forms of integrable systems at a resonant saddle, Ann. Differential Equations, 14 (1998), 150-155.
|
|
[25]
|
A. M. Lyapunov, Stability of Motion, With a contribution by V. A. Pliss and an introduction by V. P. Basov. Translated from the Russian by Flavian Abramovici and Michael Shimshoni
|
|
[26]
|
J. Llibre and X. Zhang, Polynomial first integrals for quasi-homogeneous polynomial differential systems, Nonlinearity, 15 (2002), 1269-1280.
doi: 10.1088/0951-7715/15/4/313.
|
|
[27]
|
J. F. Mattei and R. Moussu, Holonomie et intégrales premières, Ann. Sci. École Norm. Sup.
(4), 13 (1980), 469–523.
|
|
[28]
|
H. Poincaré, Mémoire sur les courbes définies par les équations différentielles, Journal de
Mathématiques, 7 (1881), 375–422; 8 (1882), 251–296; Oeuvres de Henri Poincaré, vol. I,
Gauthier-Villars, Paris, 1951, pp. 3–84.
|
|
[29]
|
M. J. Prelle and M. F. Singer, Elementary first integrals of differential equations, Trans. Amer. Math. Soc., 279 (1983), 215-229.
doi: 10.2307/1999380.
|
|
[30]
|
M. F. Singer, Liouvillian first integrals of differential equations, Trans. Amer. Math. Soc., 333 (1992), 673-688.
doi: 10.2307/2154053.
|
{{journal.titleEn}} 
DownLoad: