From b4604532d17880bab6c8846d9a1de21a4d9f3665 Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Sun, 29 Nov 2020 20:53:43 +0100 Subject: [PATCH] modif singularities --- Manuscript/EPAWTFT.tex | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/Manuscript/EPAWTFT.tex b/Manuscript/EPAWTFT.tex index 5e3f250..e9983f8 100644 --- a/Manuscript/EPAWTFT.tex +++ b/Manuscript/EPAWTFT.tex @@ -196,7 +196,8 @@ We refer the interested reader to the excellent book of Moiseyev for a general o 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 which are lines or curves 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. +Critical points are singularities which lie on the real axis and where the nature of the function undergoes a sudden transition. +However, these do not clearly belong to a given class of singularities and they cannot be rigorously classified as they have more complicated functional forms. } %%%%%%%%%%%%%%%%%%%%%%%