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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