Lundberg, Erik Limit cycle enumeration in random vector fields. (English) Zbl 1525.34058 Trans. Am. Math. Soc. 376, No. 8, 5693-5730 (2023). MSC: 34C05 34C07 60G60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Braghtha, Aymen Darboux integrable system with a triple point and pseudo-abelian integrals. (English) Zbl 1451.34035 J. Dyn. Control Syst. 26, No. 4, 761-774 (2020). MSC: 34C08 34C07 34A05 34E10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Rebollo-Perdomo, Salomón; Santibáñez, Marco Uribe Number of zeros of complete abelian integrals for a primitive rational polynomial with non-trivial global monodromy. (English) Zbl 1511.34045 Bull. Braz. Math. Soc. (N.S.) 51, No. 3, 697-717 (2020). MSC: 34C08 34C07 14K20 34C05 × Cite Format Result Cite Review PDF Full Text: DOI
Braghtha, Aymen Darboux systems with a cusp point and pseudo-abelian integrals. (English) Zbl 1440.34034 J. Differ. Equations 268, No. 3, 901-909 (2020). Reviewer: Alexey O. Remizov (Moskva) MSC: 34C08 34C07 × Cite Format Result Cite Review PDF Full Text: DOI HAL
Llibre, Jaume; Tang, Yilei Limit cycles of discontinuous piecewise quadratic and cubic polynomial perturbations of a linear center. (English) Zbl 1478.34040 Discrete Contin. Dyn. Syst., Ser. B 24, No. 4, 1769-1784 (2019). Reviewer: Stefano Marò (Pisa) MSC: 34C07 34C29 34C25 34C05 34A36 34E10 34C23 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Moghimi, Pegah; Asheghi, Rasoul; Kazemi, Rasool On the number of limit cycles bifurcated from some Hamiltonian systems with a double homoclinic loop and a heteroclinic loop. (English) Zbl 1366.34047 Int. J. Bifurcation Chaos Appl. Sci. Eng. 27, No. 4, Article ID 1750055, 15 p. (2017). MSC: 34C07 34C23 34E05 34E10 34C37 34C05 × Cite Format Result Cite Review PDF Full Text: DOI
Rebollo-Perdomo, Salomón Complete abelian integrals for polynomials whose generic fiber is biholomorphic to \(\mathbb C\). (English) Zbl 1250.32028 J. Math. Anal. Appl. 394, No. 2, 562-570 (2012). Reviewer: Vladimir P. Kostov (Nice) MSC: 32S70 × Cite Format Result Cite Review PDF Full Text: DOI
Cluckers, Raf; Miller, Daniel J. Stability under integration of sums of products of real globally subanalytic functions and their logarithms. (English) Zbl 1216.26008 Duke Math. J. 156, No. 2, 311-348 (2011). Reviewer: József Sándor (Cluj-Napoca) MSC: 26B15 14P15 32B20 03C64 14P10 33B10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gavrilov, Lubomir; Novikov, Dmitry On the finite cyclicity of open period annuli. (English) Zbl 1205.34030 Duke Math. J. 152, No. 1, 1-26 (2010). Reviewer: Maite Grau (Lleida) MSC: 34C07 34C23 34C10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Binyamini, Gal; Yakovenko, Sergei Polynomial bounds for the oscillation of solutions of Fuchsian systems. (English) Zbl 1235.34232 Ann. Inst. Fourier 59, No. 7, 2891-2926 (2009). MSC: 34M10 34C08 14Q20 32S40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv EuDML
Bobieński, Marcin; Mardešić, Pavao; Novikov, Dmitry Pseudo-abelian integrals: unfolding generic exponential case. (English) Zbl 1197.34046 J. Differ. Equations 247, No. 12, 3357-3376 (2009). Reviewer: Maite Grau (Lleida) MSC: 34C08 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Khovanskaya, I. A. Weak infinitesimal Hilbert’s 16th problem. (English. Russian original) Zbl 1351.34034 Proc. Steklov Inst. Math. 254, 201-230 (2006); translation from Tr. Mat. Inst. Steklova 254, 215-246 (2006). MSC: 34C07 37C27 37F75 × Cite Format Result Cite Review PDF Full Text: DOI
Ilyashenko, Yu. Centennial history of Hilbert’s 16th Problem. (English) Zbl 1004.34017 Bull. Am. Math. Soc., New Ser. 39, No. 3, 301-354 (2002). MSC: 34C07 34C08 34-03 × Cite Format Result Cite Review PDF Full Text: DOI
Novikov, D.; Yakovenko, S. Redundant Picard-Fuchs system for abelian integrals. (English) Zbl 1011.37042 J. Differ. Equations 177, No. 2, 267-306 (2001). Reviewer: J.M.Muñoz Porras (Salamanca) MSC: 37K20 14H70 34C07 34C08 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Novikov, D.; Yakovenko, S. Tangential Hilbert problem for perturbations of hyperelliptic Hamiltonian systems. (English) Zbl 0922.58076 Electron. Res. Announc. Am. Math. Soc. 5, No. 8, 55-65 (1999). MSC: 37N99 37G15 14K20 34M99 30C15 34C05 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Chicone, Carmen; Jacobs, Marc Bifurcation of critical periods for plane vector fields. (English) Zbl 0678.58027 Trans. Am. Math. Soc. 312, No. 2, 433-486 (1989). Reviewer: J.Šiška MSC: 37G99 37J40 34C15 × Cite Format Result Cite Review PDF Full Text: DOI
Żołądek, Henryk Bifurcations of certain family of planar vector fields tangent to axes. (English) Zbl 0648.34068 J. Differ. Equations 67, 1-55 (1987). Reviewer: A.Klič MSC: 34D30 34C05 37G99 × Cite Format Result Cite Review PDF Full Text: DOI
Khovanskij, A. G. Real analytic varieties with the finiteness property and complex abelian integrals. (English. Russian original) Zbl 0584.32016 Funct. Anal. Appl. 18, 119-127 (1984); translation from Funkts. Anal. Prilozh. 18, No. 2, 40-50 (1984). Reviewer: M.G.Eastwood MSC: 32C05 58A17 58A07 × Cite Format Result Cite Review PDF Full Text: DOI