From 98748ea4ba66f08512250777c919f39941adb2f7 Mon Sep 17 00:00:00 2001 From: "kurchan.jorge" Date: Thu, 10 Dec 2020 12:50:51 +0000 Subject: Update on Overleaf. --- bezout.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'bezout.tex') diff --git a/bezout.tex b/bezout.tex index b73732d..785e3d8 100644 --- a/bezout.tex +++ b/bezout.tex @@ -111,7 +111,7 @@ $\epsilon=H/N$, the average energy. Critical points are given by the set of equations: \begin{equation} -\frac{c_p}{(p-1)!}\sum_{ i, i_2\cdots i_p}^NJ_{i, i_2\cdots i_p}z_{i_2}\cdots z_{i_p} = \epsilon z_ +\frac{c_p}{(p-1)!}\sum_{ i, i_2\cdots i_p}^NJ_{i, i_2\cdots i_p}z_{i_2}\cdots z_{i_p} = \epsilon z_i Since $H$ is holomorphic, a point is a critical point of its real part if and -- cgit v1.2.3-54-g00ecf From 59ff2b9c61517ac7f89f38821a09ca4cf9ac28cd Mon Sep 17 00:00:00 2001 From: "kurchan.jorge" Date: Thu, 10 Dec 2020 12:51:43 +0000 Subject: Update on Overleaf. --- bezout.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) (limited to 'bezout.tex') diff --git a/bezout.tex b/bezout.tex index 785e3d8..eaed1a7 100644 --- a/bezout.tex +++ b/bezout.tex @@ -112,8 +112,8 @@ Critical points are given by the set of equations: \begin{equation} \frac{c_p}{(p-1)!}\sum_{ i, i_2\cdots i_p}^NJ_{i, i_2\cdots i_p}z_{i_2}\cdots z_{i_p} = \epsilon z_i - - +\end{equation} +which for given $\epsilon$ are a set pf $N$ equations of degree $ Since $H$ is holomorphic, a point is a critical point of its real part if and only if it is also a critical point of its imaginary part. The number of critical points of $H$ is therefore the number of critical points of -- cgit v1.2.3-54-g00ecf