Abstract
The goal of this paper is double. First, we illustrate a method for studying the bifurcation of limit cycles from the continuum periodic orbits of a k-dimensional isochronous center contained in ℝn with n ⩾ k, when we perturb it in a class of \(\mathcal{C}^2\) differential systems. The method is based in the averaging theory. Second, we consider a particular polynomial differential system in the plane having a center and a non-rational first integral. Then we study the bifurcation of limit cycles from the periodic orbits of this center when we perturb it in the class of all polynomial differential systems of a given degree. As far as we know this is one of the first examples that this study can be made for a polynomial differential system having a center and a non-rational first integral.
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The first and third authors are partially supported by a MCYT/FEDER grant MTM2005-06098-C01, and by a CIRIT grant number 2005SGR-00550. The second author is partially supported by a FAPESP–BRAZIL grant 10246-2. The first two authors are also supported by the joint project CAPES–MECD grant HBP2003-0017.
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Llibre, J., Teixeira, M.A. & Torregrosa, J. Limit Cycles Bifurcating from a k-dimensional Isochronous Center Contained in ℝn with k ⩽ n . Math Phys Anal Geom 10, 237–249 (2007). https://doi.org/10.1007/s11040-007-9030-7
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DOI: https://doi.org/10.1007/s11040-007-9030-7