The center conditions for a perturbed cubic center via the fourth-order Melnikov function
Author:
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Geometry and Topology,Algebra and Number Theory,Analysis
Link
https://link.springer.com/content/pdf/10.1007/s13398-022-01333-2.pdf
Reference11 articles.
1. Asheghi, R., Nabavi, A.: Higher order Melnikov functions for studying limit cycles of some perturbed elliptic Hamiltonian vector fields. Qual. Theory Dyn. Syst. 18, 289–313 (2019)
2. Asheghi, R., Nabavi, A.: The third order melnikov function of a cubic integrable system under quadratic perturbations. Chaos, Solitons and Fractals. 139, 110291 (2020)
3. Buică, A., Gasull, A., Yang, J.: The third order Melnikov function of a quadratic center under quadratic perturbations. J. Math. Anal. Appl. 331, 443–454 (2007)
4. Buică, A., Llibre, J.: Limit cycles of a perturbed cubic polynomial differential center. Chaos, Solitons & Fractals. 32, 1059–1069 (2007)
5. Françoise, J.P.: Successive derivatives of a first return map, application to the study of quadratic vector fields. Ergodic Theory Dyn. Syst. 16, 87–96 (1996)
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