Corrigendum: On the Abel differential equations of third kind

Figure 1.  Global phase portraits in the Poincaré disk of of system $(ⅰ)$

Figure 2.  Global phase portraits in the Poincaré disk of system $(ⅰ)$

Figure 3.  Bifurcation diagram of system $(ⅰ)$ for $ k_1 = 1 $ and $ k_1 = 0 $. The phase portrait $ P_2 $ is topologically equivalent to $ L_{8} $. In this diagram, the phase portraits in the surfaces $ S_i $, for $ i = 4, 5, 6, 9, 10, 18 $ and in the curves $ L_j $, for $ j = 2, 4, 5, 6 $ admit a separatrix connection and although such surfaces and curves do not need to be algebraic the surfaces $ S_9 $ and $ S_{10} $ are contained in one component of the algebraic surface given by $ -64 k_0^3 - k_1^6 + 16 k_0^2 k_1^2 k_2 - 3 k_0 k_1^4 k_2^2 + 16 k_0^3 k_2^3 - 3 k_0^2 k_1^2 k_2^4 - k_0^3 k_2^6 = 0 $

Figure 4.  Global phase portraits in the Poincaré disk of systems $(ⅱ)$. The phase portraits $ V_{13} $ and $ V_{15} $ of system $(ⅱ)$ are topologically equivalent to the phase portraits $ S_3 $ and $ S_2 $ of system $(ⅰ)$, respectively. Here we remark that in the phase portraits $ S_3 $ and $ S_2 $ of system $(ⅰ)$, such system has two complex points and a saddle–node as finite singular points but in system $(ⅱ)$ the phase portraits $ V_{13} $ and $ V_{15} $ have a saddle–node as the unique finite singular point. The phase portrait $ S_{21} $ has a separatrix connection between the finite saddle-node and the infinite saddle