The notion of persistent center has recently been extended to a linearizable persistent centers. We define the linearizability of persistent p:−q resonant center and explain the relation between p:−q ...resonant system and the corresponding persistent p:−q resonant system in terms of integrability and linearizability problems. We demonstrate the obtained results for persistent p:−q resonant systems with quadratic nonlinearities for p=1, q=2 and p=2, q=3.
The notion of $p:-q$ resonant center was introduced recently and studied by several authors. In this paper we generalize the notion of a persistent center to a persistent $p:-q $ resonant center and ...find conditions for existence of a persistent $p:-q$ resonant center for several $p:-q$ resonant systems with quadratic nonlinearities. To prove the sufficiency of the obtained conditions we use either the Darboux theory of integrability or look for a formal first integral of the required form or we use the method based on the blow-up transformation.
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