I am studying Chapter 5, section 2.3 of the book "Stability Theory by Lyapunov's Direct Method" by Laloy, Rouche & Habets.
In section 4 of Chapter 5 there is a coment "Sectors and absolute sectors will often be characterized by the way solutions of the differential equations cross their side boundary. They can cross it all from outside to inside and this type of behavior leads to absolute sectors, or all from inside to outside and this yields sectors, or, in a more complicated way, some from outside to inside and the others from inside to outside." The authors also coment that an absolute sector do not have to be an expeller.
I am having some problem understanding the definition of an absolute sector (given in section 2.3 of Chapter 5, and uses some definitions and hypothesis of previous chapters), there is no image in the book describing such sectors. More precisely I am trying to understand this definition in order to prove that a certain set is an absolute sector (the set in question is given at section 2.14 of Chapter 3).
So I would like to know there is other books, pdfs which talk about absolute sectors? I tried search online but couldn't find.
Any help is appreciated.