The material we need for the Poincare-Bendixson Theorem is covered in chapter 10 of Differential equations, dynamical systems and an introduction to chaos by M.W. Hirisch, S. Smale and R.L. Devaney. Please be aware that the entire book can be consulted digitally from the Imperial library website (where this chapter can also be downloaded; just search for the authors on the Library search and you find a link to the digitcal copy). For your convenience, I also created a temporary link in the left-hand side margin, under chapter 5.
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