Abstract
We prove that there are one-parameter families of planar differential equations for which the center problem has a trivial solution and on the other hand the cyclicity of the weak focus is arbitrarily high. We illustrate this phenomenon in several examples for which this cyclicity is computed.
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In memory of Javier Chavarriga.
A. Gasull is partially supported by a MCYT/FEDER grant number MTM2008-03437 and by a CIRIT grant number 2009SGR 410. J. Giné is partially supported by a MCYT/FEDER grant number MTM2008-00694 and by a CIRIT grant number 2009SGR 381.
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Gasull, A., Giné, J. Cyclicity versus Center Problem. Qual. Theory Dyn. Syst. 9, 101–113 (2010). https://doi.org/10.1007/s12346-010-0022-9
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DOI: https://doi.org/10.1007/s12346-010-0022-9