Zhou, Jinping; Zhao, Liqin; Wang, Jiaxin Cyclicity of a class of Hamiltonian systems under perturbations of piecewise smooth polynomials. (English) Zbl 1486.37032 Int. J. Bifurcation Chaos Appl. Sci. Eng. 31, No. 13, Article ID 2150199, 14 p. (2021). Reviewer: Iliya Iliev (Sofia) MSC: 37J40 37J20 34C07 34C08 PDFBibTeX XMLCite \textit{J. Zhou} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 31, No. 13, Article ID 2150199, 14 p. (2021; Zbl 1486.37032) Full Text: DOI
Yang, Jihua Limit cycles of a kind of nonsmooth differential systems with two switching lines. (English) Zbl 1461.34053 Int. J. Bifurcation Chaos Appl. Sci. Eng. 31, No. 6, Article ID 2150095, 15 p. (2021). MSC: 34C05 37G15 34C23 PDFBibTeX XMLCite \textit{J. Yang}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 31, No. 6, Article ID 2150095, 15 p. (2021; Zbl 1461.34053) Full Text: DOI
Chen, Aiyong; Zhang, Huiyang The number of zeros of abelian integral for a quintic Hamiltonian systems with a rose-figure loop. (English) Zbl 1499.34227 J. Dyn. Syst. Geom. Theor. 18, No. 1, 97-109 (2020). MSC: 34C08 37J46 34C07 PDFBibTeX XMLCite \textit{A. Chen} and \textit{H. Zhang}, J. Dyn. Syst. Geom. Theor. 18, No. 1, 97--109 (2020; Zbl 1499.34227) Full Text: DOI
Yang, Jihua; Zhang, Erli On the number of limit cycles for a class of piecewise smooth Hamiltonian systems with discontinuous perturbations. (English) Zbl 1472.34026 Nonlinear Anal., Real World Appl. 52, Article ID 103046, 10 p. (2020). Reviewer: Valery A. Gaiko (Minsk) MSC: 34A36 34E10 34C05 37J40 34C07 PDFBibTeX XMLCite \textit{J. Yang} and \textit{E. Zhang}, Nonlinear Anal., Real World Appl. 52, Article ID 103046, 10 p. (2020; Zbl 1472.34026) Full Text: DOI
Yang, Jihua; Sui, Shiyou; Zhao, Liqin On the number of zeros of abelian integral for a class of cubic Hamilton systems with the phase portrait “butterfly”. (English) Zbl 1431.34043 Qual. Theory Dyn. Syst. 18, No. 3, 947-967 (2019). MSC: 34C08 34E10 37J40 34C07 34C23 PDFBibTeX XMLCite \textit{J. Yang} et al., Qual. Theory Dyn. Syst. 18, No. 3, 947--967 (2019; Zbl 1431.34043) Full Text: DOI
Yang, Jihua On the number of zeros of abelian integral for a class of cubic Hamiltonian systems. (English) Zbl 1440.34035 Dyn. Syst. 34, No. 4, 561-583 (2019). Reviewer: Valery A. Gaiko (Minsk) MSC: 34C08 37J40 34C07 PDFBibTeX XMLCite \textit{J. Yang}, Dyn. Syst. 34, No. 4, 561--583 (2019; Zbl 1440.34035) Full Text: DOI
Dai, Jialiang; Fan, Engui Whitham hierarchy and generalized Picard-Fuchs operators in the \(\mathcal{N}=2\) susy Yang-Mills theory for classical gauge groups. (English. Russian original) Zbl 1419.81031 Theor. Math. Phys. 198, No. 3, 317-330 (2019); translation from Teor. Mat. Fiz. 198, No. 3, 365-380 (2019). MSC: 81T13 81T60 37K10 14H52 81T17 57R57 14D21 PDFBibTeX XMLCite \textit{J. Dai} and \textit{E. Fan}, Theor. Math. Phys. 198, No. 3, 317--330 (2019; Zbl 1419.81031); translation from Teor. Mat. Fiz. 198, No. 3, 365--380 (2019) Full Text: DOI
Yang, Jihua On the algebraic structure and the number of zeros of abelian integral for a class of Hamiltonians with degenerate singularities. (English) Zbl 1447.34034 Bull. Braz. Math. Soc. (N.S.) 49, No. 4, 893-913 (2018). Reviewer: Caidi Zhao (Wenzhou) MSC: 34C08 37J40 PDFBibTeX XMLCite \textit{J. Yang}, Bull. Braz. Math. Soc. (N.S.) 49, No. 4, 893--913 (2018; Zbl 1447.34034) Full Text: DOI
Gavrilov, Lubomir Irreducibility of the Picard-Fuchs equation related to the Lotka-Volterra polynomial \(x^2y^2(1-x-y)\). (English) Zbl 1403.37056 J. Dyn. Control Syst. 24, No. 3, 425-438 (2018). Reviewer: Jesus Muciño-Raymundo (Morelia) MSC: 37F75 34C05 37J05 37J35 PDFBibTeX XMLCite \textit{L. Gavrilov}, J. Dyn. Control Syst. 24, No. 3, 425--438 (2018; Zbl 1403.37056) Full Text: DOI arXiv
Zhang, Erli; Xing, Yuqing Limit cycle bifurcations for a kind of Hamilton systems of degree three. (Chinese. English summary) Zbl 1399.37033 Acta Math. Sci., Ser. A, Chin. Ed. 37, No. 5, 825-833 (2017). MSC: 37J20 37G15 34C07 PDFBibTeX XMLCite \textit{E. Zhang} and \textit{Y. Xing}, Acta Math. Sci., Ser. A, Chin. Ed. 37, No. 5, 825--833 (2017; Zbl 1399.37033)
Ma, Huilong; Yang, Jihua On the number of zeros for Abel integrals of Hamilton system of seven degree with nilpotent singularities. (Chinese. English summary) Zbl 1399.34099 J. Math., Wuhan Univ. 37, No. 6, 1227-1233 (2017). MSC: 34C08 34C05 37J45 PDFBibTeX XMLCite \textit{H. Ma} and \textit{J. Yang}, J. Math., Wuhan Univ. 37, No. 6, 1227--1233 (2017; Zbl 1399.34099) Full Text: DOI
Yang, Jihua; Shang, Huahui On the number of zeros of abelian integrals for a kind of Hamiltonian systems of degree three. (Chinese. English summary) Zbl 1389.34104 J. Nat. Sci. Heilongjiang Univ. 34, No. 3, 291-296 (2017). MSC: 34C08 34C07 37J40 34E10 PDFBibTeX XMLCite \textit{J. Yang} and \textit{H. Shang}, J. Nat. Sci. Heilongjiang Univ. 34, No. 3, 291--296 (2017; Zbl 1389.34104) Full Text: DOI
Bai, Long; Yang, Jihua Linear estimate for the number of zeros of abelian integrals of Hamiltonian system with singular line. (Chinese. English summary) Zbl 1389.34103 J. Northwest Norm. Univ., Nat. Sci. 53, No. 2, 13-16, 20 (2017). MSC: 34C08 37J45 PDFBibTeX XMLCite \textit{L. Bai} and \textit{J. Yang}, J. Northwest Norm. Univ., Nat. Sci. 53, No. 2, 13--16, 20 (2017; Zbl 1389.34103) Full Text: DOI
Yang, Jihua; Zhang, Erli; Liu, Mei The cyclicity of period annuli of a class of quartic Hamiltonian systems. (Chinese. English summary) Zbl 1389.37038 Adv. Math., Beijing 46, No. 2, 243-251 (2017). MSC: 37J45 34C05 34C07 34D10 PDFBibTeX XMLCite \textit{J. Yang} et al., Adv. Math., Beijing 46, No. 2, 243--251 (2017; Zbl 1389.37038)
Yang, Jihua; Liu, Mei; He, Zhicheng The number of zeros of abelian integrals for a kind of quartic Hamiltonians with a nilpotent center. (Chinese. English summary) Zbl 1374.34095 Acta Math. Sci., Ser. A, Chin. Ed. 36, No. 5, 937-945 (2016). MSC: 34C08 34C05 37J40 PDFBibTeX XMLCite \textit{J. Yang} et al., Acta Math. Sci., Ser. A, Chin. Ed. 36, No. 5, 937--945 (2016; Zbl 1374.34095)
Nikdelan, Younes Darboux-Halphen-Ramanujan vector field on a moduli of Calabi-Yau manifolds. (English) Zbl 1349.53097 Qual. Theory Dyn. Syst. 14, No. 1, 71-100 (2015). MSC: 53C55 14J15 14J32 32G20 14C30 14D07 34M45 37F75 PDFBibTeX XMLCite \textit{Y. Nikdelan}, Qual. Theory Dyn. Syst. 14, No. 1, 71--100 (2015; Zbl 1349.53097) Full Text: DOI arXiv
Zhao, Li Qin; Li, De Ping Bifurcations of limit cycles from a quintic Hamiltonian system with a heteroclinic cycle. (English) Zbl 1301.34057 Acta Math. Sin., Engl. Ser. 30, No. 3, 411-422 (2014). Reviewer: Alexander Grin (Grodno) MSC: 34C23 34C05 34C37 37J45 PDFBibTeX XMLCite \textit{L. Q. Zhao} and \textit{D. P. Li}, Acta Math. Sin., Engl. Ser. 30, No. 3, 411--422 (2014; Zbl 1301.34057) Full Text: DOI
Fedorov, Yuri; Pantazi, Chara The Picard-Fuchs equations for complete hyperelliptic integrals of even order curves, and the actions of the generalized Neumann system. (English) Zbl 1298.14037 J. Math. Phys. 55, No. 3, 032703, 8 p. (2014). Reviewer: Bujar Fejzullahu (Presevo) MSC: 14H70 34M03 34M56 37J35 PDFBibTeX XMLCite \textit{Y. Fedorov} and \textit{C. Pantazi}, J. Math. Phys. 55, No. 3, 032703, 8 p. (2014; Zbl 1298.14037) Full Text: DOI arXiv
Papadopoulos, George; Dullin, Holger R. Semi-global symplectic invariants of the Euler top. (English) Zbl 1334.37055 J. Geom. Mech. 5, No. 2, 215-232 (2013). MSC: 37J15 70E15 70E40 70H06 37J35 34M45 PDFBibTeX XMLCite \textit{G. Papadopoulos} and \textit{H. R. Dullin}, J. Geom. Mech. 5, No. 2, 215--232 (2013; Zbl 1334.37055) Full Text: DOI arXiv
Hong, Chun; Zou, Lan Abelian integrals and critical periods for a class of reversible quadratic systems. (Chinese. English summary) Zbl 1274.34095 J. Sichuan Univ., Nat. Sci. Ed. 49, No. 5, 960-964 (2012). MSC: 34C08 37J45 34C25 34C05 34C14 PDFBibTeX XMLCite \textit{C. Hong} and \textit{L. Zou}, J. Sichuan Univ., Nat. Sci. Ed. 49, No. 5, 960--964 (2012; Zbl 1274.34095) Full Text: DOI
Gao, Bo; He, Zhirong Limit cycles of a class of planar system with \(1:2\) resonance for linear cusp. (Chinese. English summary) Zbl 1212.34101 J. Sichuan Univ., Nat. Sci. Ed. 46, No. 5, 1224-1228 (2009). MSC: 34C05 34C07 37G10 37G15 34C23 34C37 34E10 PDFBibTeX XMLCite \textit{B. Gao} and \textit{Z. He}, J. Sichuan Univ., Nat. Sci. Ed. 46, No. 5, 1224--1228 (2009; Zbl 1212.34101)
He, Zhirong; Zhang, Weinian Critical periods of a periodic annulus linking to equilibria at infinity in a cubic system. (English) Zbl 1180.34034 Discrete Contin. Dyn. Syst. 24, No. 3, 841-854 (2009). Reviewer: Valery A. Gaiko (Minsk) MSC: 34C08 37J45 34C05 PDFBibTeX XMLCite \textit{Z. He} and \textit{W. Zhang}, Discrete Contin. Dyn. Syst. 24, No. 3, 841--854 (2009; Zbl 1180.34034) Full Text: DOI
Song, Yan The Poincaré bifurcation of cubic non-Hamiltonian integrable systems with double centers. (Chinese. English summary) Zbl 1174.34394 Chin. J. Eng. Math. 25, No. 4, 679-684 (2008). MSC: 34C23 34C08 34C05 37G10 PDFBibTeX XMLCite \textit{Y. Song}, Chin. J. Eng. Math. 25, No. 4, 679--684 (2008; Zbl 1174.34394)
Zhou, Xin; Li, Cuiping Estimate of the number of zeros of abelian integrals for a kind of quartic Hamiltonians with two centers. (English) Zbl 1156.37013 Appl. Math. Comput. 204, No. 1, 202-209 (2008). Reviewer: Christian Pötzsche (München) MSC: 37J20 37G15 PDFBibTeX XMLCite \textit{X. Zhou} and \textit{C. Li}, Appl. Math. Comput. 204, No. 1, 202--209 (2008; Zbl 1156.37013) Full Text: DOI
Song, Yan Estimation on the number of zeros of Abelian integrals of a planar Hamiltonian system. (Chinese. English summary) Zbl 1063.34027 J. Math. Res. Expo. 23, No. 4, 651-657 (2003). MSC: 34C08 37G15 PDFBibTeX XMLCite \textit{Y. Song}, J. Math. Res. Expo. 23, No. 4, 651--657 (2003; Zbl 1063.34027)
Dullin, Holger R.; Richter, Peter H.; Veselov, Alexander P.; Waalkens, Holger Actions of the Neumann systems via Picard-Fuchs equations. (English) Zbl 1001.70013 Physica D 155, No. 3-4, 159-183 (2001). MSC: 70H06 37N05 PDFBibTeX XMLCite \textit{H. R. Dullin} et al., Physica D 155, No. 3--4, 159--183 (2001; Zbl 1001.70013) Full Text: DOI
Zhao, Yulin; Zhang, Zhifen An estimate of the number of zeros of Abelian integrals for cubic vector fields with cuspidal loop. (English) Zbl 0967.34027 Ann. Differ. Equations 14, No. 2, 434-445 (1998). MSC: 34C08 14K20 34C05 34C23 37G15 PDFBibTeX XMLCite \textit{Y. Zhao} and \textit{Z. Zhang}, Ann. Differ. Equations 14, No. 2, 434--445 (1998; Zbl 0967.34027)
Horozov, Emil; Iliev, Iliya D. Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians. (English) Zbl 0921.58044 Nonlinearity 11, No. 6, 1521-1537 (1998). Reviewer: E.Ershov (St.Peterburg) MSC: 37G15 37J20 37K50 34C05 PDFBibTeX XMLCite \textit{E. Horozov} and \textit{I. D. Iliev}, Nonlinearity 11, No. 6, 1521--1537 (1998; Zbl 0921.58044) Full Text: DOI
Zhang, Zhifen; Li, Chengzhi On the number of limit cycles of a class of quadratic Hamiltonian systems under quadratic perturbations. (English) Zbl 0948.34020 Adv. Math., Beijing 26, No. 5, 445-460 (1997). Reviewer: Dmitry Turaev (Berlin) MSC: 34C07 37G15 34C23 PDFBibTeX XMLCite \textit{Z. Zhang} and \textit{C. Li}, Adv. Math., Beijing 26, No. 5, 445--460 (1997; Zbl 0948.34020)
van Gils, S. A. An inhomogeneous Picard-Fuchs equation. (English) Zbl 0810.58033 Chossat, Pascal (ed.), Dynamics, bifurcation and symmetry. New trends and new tools. Proceedings of the NATO Advanced Research Workshop, E. B. T. G. Conference, Cargèse, France, September 3-9, 1993. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. C, Math. Phys. Sci. 437, 333-341 (1994). Reviewer: Z.Denkowska (Angers) MSC: 37G15 34C05 PDFBibTeX XMLCite \textit{S. A. van Gils}, NATO ASI Ser., Ser. C, Math. Phys. Sci. 437, 333--341 (1994; Zbl 0810.58033)
Chow, Shiu-Nee; Li, Chengzhi; Wang, Duo A simple proof of the uniqueness of periodic orbits in the 1:3 resonance problem. (English) Zbl 0691.58028 Proc. Am. Math. Soc. 105, No. 4, 1025-1032 (1989). Reviewer: K.Chang MSC: 37G99 34C05 PDFBibTeX XMLCite \textit{S.-N. Chow} et al., Proc. Am. Math. Soc. 105, No. 4, 1025--1032 (1989; Zbl 0691.58028) Full Text: DOI
Sanders, Jan A.; Cushman, Richard Limit cycles in the Josephson equation. (English) Zbl 0604.58041 SIAM J. Math. Anal. 17, 495-511 (1986). Reviewer: J.Kalas MSC: 37G15 34C29 37G99 34C05 PDFBibTeX XMLCite \textit{J. A. Sanders} and \textit{R. Cushman}, SIAM J. Math. Anal. 17, 495--511 (1986; Zbl 0604.58041) Full Text: DOI
Françoise, Jean-Pierre Sur les action-angles de la toupie de Kowalevski. (The action-angles of the Kowalevski top). (French) Zbl 0588.58024 C. R. Acad. Sci., Paris, Sér. I 300, 427-430 (1985). Reviewer: W.M.Oliva MSC: 37J99 PDFBibTeX XMLCite \textit{J.-P. Françoise}, C. R. Acad. Sci., Paris, Sér. I 300, 427--430 (1985; Zbl 0588.58024)