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Bifurcations from a normally degenerate cycle in forced planar differential equations

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Abstract

Bifurcations from a resonant period manifold in forced systems are intensively studied in the literature, usually assuming that the period manifold is normally non-degenerate. This paper deals with smooth systems in dimension two, considering bifurcations from a normally degenerate cycle. The complexity of this situation is characterized in terms of the Poincaré return map and return-time map near the cycle of the unperturbed system. A geometric setting is defined to analyze the Poincaré translation map of the perturbed system. Our main result presents the degenerate situation in deep, clear and essential terms.

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Acknowledgements

This work was supported by a grant of the Ministry of Research, Innovation and Digitization, CNCS/CCCDI—UEFISCDI, project number PN-III-P1-1.1-TE-2019-1306, within PNCDI III. We are also grateful to the anonymous referees for their comments which helped to improve the presentation of this paper.

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  1. Departamentul de Matematică, Universitatea Babeş–Bolyai, Str. Kogălniceanu 1, 400084, Cluj–Napoca, Romania

    Adriana Buică

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  1. Adriana Buică
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Buică, A. Bifurcations from a normally degenerate cycle in forced planar differential equations. Nonlinear Differ. Equ. Appl. 30, 63 (2023). https://doi.org/10.1007/s00030-023-00868-6

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