added small paragraph on singularities

Manuscript/EPAWTFT.tex

@@ -191,6 +191,13 @@ More importantly here, although EPs usually lie off the real axis, these singula
 Through a complex-scaling of the electronic or atomic coordinates,\cite{Moiseyev_1998} or by introducing a complex absorbing potential,\cite{Riss_1993,Ernzerhof_2006,Benda_2018} outgoing resonance states are transformed into square-integrable wave functions that allow the energy and lifetime of the resonance to be computed.
 We refer the interested reader to the excellent book of Moiseyev for a general overview. \cite{MoiseyevBook}}
 
+\titou{Discussion around the different types of singularities in complex analysis.
+At a singular point, a function and/or its derivatives becomes infinite or undefined (hence non analytic).
+One very common type of singularities (belonging to the family of isolated singularities) are poles where the function behaves $1/(\lambda - \lambda_c)^n$ where $n \in \mathbb{N}^*$ is the order of the pole.
+Another class of singularities are branch points resulting from a multi-valued function such as a square root or a logarithm function and usually implying the presence of so-called branch cuts where the function ``jumps'' from one value to another.
+Yet another family of singularities are formed by critical points which lie on the real axis, have more complicated functional forms and where the nature of the function undergoes a sudden transition.
+}
+
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 \section{Exceptional Points in Electronic Structure}
 \label{sec:EPs}