Abstract
We studyC 1 perturbations of a reversible polynomial differential system of degree 4 in\(\mathbb{R}^3 \). We introduce the concept of strongly reversible vector field. If the perturbation is strongly reversible, the dynamics of the perturbed system does not change. For non-strongly reversible perturbations we prove the existence of an arbitrary number of symmetric periodic orbits. Additionally, we provide a polynomial vector field of degree 4 in\(\mathbb{R}^3 \) with infinitely many limit cycles in a bounded domain if a generic assumption is satisfied.
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The first two authors are partially supported by a MCYT grant number MTM2005-06098-C02-01, and by a CICYT grant number 2005SGR 00550. The second author is partially supported by a FAPESP-BRAZIL grant 10246-2. All authors are also supported by the joint project CAPES-MECD grant HBP2003-0017.
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Ferragut, A., Llibre, J. & Teixeira, M.A. Periodic orbits for a class ofC 1 three-dimensional systems. Rend. Circ. Mat. Palermo 56, 101–115 (2007). https://doi.org/10.1007/BF03031432
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DOI: https://doi.org/10.1007/BF03031432