TY - JOUR AU - Qiu, J. AU - Li, F. PY - 2015 DA - 2015// TI - Two kinds of bifurcation phenomena in a quartic system JO - Adv. Differ. Equ. VL - 2015 UR - https://doi.org/10.1186/s13662-014-0331-4 DO - 10.1186/s13662-014-0331-4 ID - Qiu2015 ER - TY - JOUR AU - Zhang, Z. AU - Li, C. PY - 1992 DA - 1992// TI - On the number of limit cycles of a class of quadratic Hamiltonian systems under quadratic perturbations JO - Adv. Math. VL - 26 ID - Zhang1992 ER - TY - BOOK AU - Amelikin, B. B. AU - Lukashivich, H. A. AU - Sadovski, A. P. PY - 1992 DA - 1992// TI - Nonlinear Oscillations in Second Order Systems PB - BGY lenin.B. I. Press CY - Minsk ID - Amelikin1992 ER - TY - JOUR AU - Han, M. AU - Shu, C. AU - Yang, J. PY - 2010 DA - 2010// TI - Polynomial Hamiltonian systems with a nilpotent critical point JO - Adv. Space Res. VL - 46 UR - https://doi.org/10.1016/j.asr.2008.08.025 DO - 10.1016/j.asr.2008.08.025 ID - Han2010 ER - TY - JOUR AU - Jiang, J. AU - Zhang, J. AU - Han, M. PY - 2009 DA - 2009// TI - Limit cycles for a class of quintic near-Hamiltonian systems near a nilpotent center JO - Int. J. Bifurc. Chaos VL - 19 UR - https://doi.org/10.1142/S0218127409023949 DO - 10.1142/S0218127409023949 ID - Jiang2009 ER - TY - JOUR AU - Yang, J. AU - Han, M. PY - 2010 DA - 2010// TI - Limit cycle bifurcations of some Liénard systems with a nilpotent cusp JO - Int. J. Bifurc. Chaos VL - 20 UR - https://doi.org/10.1142/S0218127410028045 DO - 10.1142/S0218127410028045 ID - Yang2010 ER - TY - JOUR AU - Han, M. AU - Yang, J. AU - Xiao, D. PY - 2012 DA - 2012// TI - Limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle JO - Int. J. Bifurc. Chaos VL - 22 UR - https://doi.org/10.1142/S0218127412501891 DO - 10.1142/S0218127412501891 ID - Han2012 ER - TY - JOUR AU - An, Y. AU - Han, M. PY - 2015 DA - 2015// TI - On the number of limit cycles near a homoclinic loop with a nilpotent singular point JO - J. Differ. Equ. VL - 258 UR - https://doi.org/10.1016/j.jde.2015.01.006 DO - 10.1016/j.jde.2015.01.006 ID - An2015 ER - TY - JOUR AU - Giacomini, H. AU - Gine, J. AU - Llibre, J. PY - 2006 DA - 2006// TI - The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems JO - J. Differ. Equ. VL - 227 UR - https://doi.org/10.1016/j.jde.2006.03.012 DO - 10.1016/j.jde.2006.03.012 ID - Giacomini2006 ER - TY - JOUR AU - Algaba, A. AU - García, C. AU - Reyes, M. PY - 2008 DA - 2008// TI - The center problem for a family of systems of differential equations having a nilpotent singular point JO - J. Math. Anal. Appl. VL - 340 UR - https://doi.org/10.1016/j.jmaa.2007.07.043 DO - 10.1016/j.jmaa.2007.07.043 ID - Algaba2008 ER - TY - JOUR AU - Han, M. AU - Sheng, L. AU - Zhang, X. PY - 2018 DA - 2018// TI - Bifurcation theory for finitely smooth planar autonomous differential systems JO - J. Differ. Equ. VL - 264 UR - https://doi.org/10.1016/j.jde.2017.11.025 DO - 10.1016/j.jde.2017.11.025 ID - Han2018 ER - TY - JOUR AU - Han, M. AU - Hou, X. AU - Sheng, L. AU - Wang, C. PY - 2018 DA - 2018// TI - Theory of rotated equations and applications to a population model JO - Discrete Contin. Dyn. Syst., Ser. A VL - 34 UR - https://doi.org/10.3934/dcds.2018089 DO - 10.3934/dcds.2018089 ID - Han2018 ER - TY - JOUR AU - Algaba, A. AU - García, C. AU - Gine, J. PY - 2016 DA - 2016// TI - Nilpotent centers via inverse integrating factors JO - Eur. J. Appl. Math. VL - 27 UR - https://doi.org/10.1017/S0956792516000103 DO - 10.1017/S0956792516000103 ID - Algaba2016 ER - TY - JOUR AU - Liu, Y. AU - Li, J. PY - 2009 DA - 2009// TI - New study on the center problem and bifurcations of limit cycles for the Lyapunov system (I) JO - Int. J. Bifurc. Chaos VL - 19 UR - https://doi.org/10.1142/S0218127409025110 DO - 10.1142/S0218127409025110 ID - Liu2009 ER - TY - JOUR AU - Liu, Y. AU - Li, J. PY - 2009 DA - 2009// TI - New study on the center problem and bifurcations of limit cycles for the Lyapunov system (II) JO - Int. J. Bifurc. Chaos VL - 19 UR - https://doi.org/10.1142/S0218127409024669 DO - 10.1142/S0218127409024669 ID - Liu2009 ER - TY - JOUR AU - Liu, Y. AU - Li, J. PY - 2010 DA - 2010// TI - Bifurcations of limit cycles and center problem for a class of cubic nilpotent system JO - Int. J. Bifurc. Chaos VL - 20 UR - https://doi.org/10.1142/S0218127410027210 DO - 10.1142/S0218127410027210 ID - Liu2010 ER - TY - JOUR AU - Liu, Y. AU - Li, F. PY - 2015 DA - 2015// TI - Double bifurcation of nilpotent focus JO - Int. J. Bifurc. Chaos VL - 25 UR - https://doi.org/10.1142/S0218127415500364 DO - 10.1142/S0218127415500364 ID - Liu2015 ER - TY - JOUR AU - Liu, T. AU - Wu, L. AU - Li, F. PY - 2012 DA - 2012// TI - Analytic center of nilpotent critical points JO - Int. J. Bifurc. Chaos VL - 22 UR - https://doi.org/10.1142/S0218127412501982 DO - 10.1142/S0218127412501982 ID - Liu2012 ER - TY - JOUR AU - Li, F. PY - 2012 DA - 2012// TI - Bifurcations of limit cycles in a quintic Lyapunov system with eleven parameters JO - Chaos Solitons Fractals VL - 45 UR - https://doi.org/10.1016/j.chaos.2012.07.014 DO - 10.1016/j.chaos.2012.07.014 ID - Li2012 ER - TY - JOUR AU - Li, F. AU - Liu, Y. AU - Li, H. PY - 2011 DA - 2011// TI - Center conditions and bifurcation of limit cycles at three-order nilpotent critical point in a septic Lyapunov system JO - Math. Comput. Simul. VL - 81 UR - https://doi.org/10.1016/j.matcom.2011.05.001 DO - 10.1016/j.matcom.2011.05.001 ID - Li2011 ER - TY - JOUR AU - Takens, F. PY - 1974 DA - 1974// TI - Singularities of vector fields JO - Publ. Math. IHES VL - 43 UR - https://doi.org/10.1007/BF02684366 DO - 10.1007/BF02684366 ID - Takens1974 ER - TY - JOUR AU - Strozyna, E. AU - Zoladek, H. PY - 2002 DA - 2002// TI - The analytic normal for the nilpotent singularity JO - J. Differ. Equ. VL - 179 UR - https://doi.org/10.1006/jdeq.2001.4043 DO - 10.1006/jdeq.2001.4043 ID - Strozyna2002 ER - TY - JOUR AU - Moussu, R. PY - 1982 DA - 1982// TI - Symétrie et forme normale des centres et foyers degeneres JO - Ergod. Theory Dyn. Syst. VL - 2 UR - https://doi.org/10.1017/S0143385700001553 DO - 10.1017/S0143385700001553 ID - Moussu1982 ER - TY - JOUR AU - Alvarez, M. J. AU - Gasull, A. PY - 2005 DA - 2005// TI - Monodromy and stability for nilpotent critical points JO - Int. J. Bifurc. Chaos VL - 15 UR - https://doi.org/10.1142/S0218127405012740 DO - 10.1142/S0218127405012740 ID - Alvarez2005 ER - TY - CHAP AU - Gamero, E. AU - Freire, E. AU - Ponce, E. PY - 1991 DA - 1991// TI - Normal forms for planar systems with nilpotent linear part, Bifurcation and chaos BT - Analysis, Algorithms, Applications PB - Birkhäuser CY - Basel ID - Gamero1991 ER - TY - JOUR AU - Alvarez, M. J. AU - Gasull, A. PY - 2006 DA - 2006// TI - Generating limits cycles from a nilpotent critical point via normal forms JO - J. Math. Anal. Appl. VL - 318 UR - https://doi.org/10.1016/j.jmaa.2005.05.064 DO - 10.1016/j.jmaa.2005.05.064 ID - Alvarez2006 ER - TY - STD TI - Colak, I.E.: Hamiltonian linear type centers and nilpotent centers of linear plus cubic polynomial vector fields. Ph.D. thesis, Universitat Autònoma de Barcelona (2014) ID - ref27 ER - TY - JOUR AU - Yu, P. AU - Li, F. PY - 2017 DA - 2017// TI - Bifurcation of limit cycles in a cubic-order planar system around a nilpotent critical point JO - J. Math. Anal. Appl. VL - 453 UR - https://doi.org/10.1016/j.jmaa.2017.04.019 DO - 10.1016/j.jmaa.2017.04.019 ID - Yu2017 ER - TY - JOUR AU - Bautin, N. PY - 1952 DA - 1952// TI - On the number of limit cycles which appear with the variation of coefficients from an equilibrium position of focus or center type JO - Math. Sb. (N.S.) VL - 30 ID - Bautin1952 ER - TY - JOUR AU - Zoldek, H. PY - 1995 DA - 1995// TI - Eleven small limit cycles in a cubic vector field JO - Nonlinearity VL - 8 UR - https://doi.org/10.1088/0951-7715/8/5/011 DO - 10.1088/0951-7715/8/5/011 ID - Zoldek1995 ER - TY - CHAP AU - Christopher, C. PY - 2005 DA - 2005// TI - Estimating limit cycle bifurcations from centers BT - Differential Equations with Symbolic Computation PB - Birkhäuser CY - Basel UR - https://doi.org/10.1007/3-7643-7429-2_2 DO - 10.1007/3-7643-7429-2_2 ID - Christopher2005 ER - TY - JOUR AU - Gine, J. PY - 2012 DA - 2012// TI - Higher order limit cycle bifurcations from non-degenerate centers JO - Appl. Math. Comput. VL - 218 ID - Gine2012 ER -