Cyclicity of lips and center-focus problem near infinity
In this work, we discover an intriguing Liénard system which is integrable near infinity, integrable near zero and having Ilyashenko-Kotova lips in between. Moreover, we give a necessary and sufficient condition of polynomial Liénard system with center at infinity. In a different direction we improve a lower bound on Hilbert number for Liénard systems. The improvement is due to development of Brudnyi method of calculation of cyclicity of centers near infinity and near zero.
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