View source for Bendixson transformation

The mapping

<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b015/b015550/b0155501.png" /></td> </tr></table>

of the Euclidean <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b015/b015550/b0155502.png" />-plane punctured at the point <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b015/b015550/b0155503.png" /> into a similar Euclidean <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b015/b015550/b0155504.png" />-plane. It is the coordinate expression of the bijection <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b015/b015550/b0155505.png" /> generated by the [[Bendixson sphere|Bendixson sphere]]. If the planes <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b015/b015550/b0155506.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b015/b015550/b0155507.png" /> coincide, the Bendixson transformation is the inversion of the plane <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b015/b015550/b0155508.png" /> with respect to the circle <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b015/b015550/b0155509.png" />.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  A.A. Andronov,   E.A. Leontovich,   I.I. Gordon,   A.G. Maier,   "Qualitative theory of second-order dynamic systems" , Wiley  (1973)  (Translated from Russian)</TD></TR></table>