From bad2736668d7ddd93e9c98bc287f530ca1cf85cc Mon Sep 17 00:00:00 2001
From: Astrid Giuliani <astrid.giuliani@etu.inp-n7.fr>
Date: Tue, 9 Jul 2024 19:15:11 +0200
Subject: [PATCH] fix index.md

---
 docs/src/index.md | 39 +++++++++++++++++++--------------------
 1 file changed, 19 insertions(+), 20 deletions(-)

diff --git a/docs/src/index.md b/docs/src/index.md
index df0973a..06a867c 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -1,30 +1,29 @@
 # The averaged Kepler problem
 
-```
+
 We consider the Hamiltonian
 
-$$
-    H(r, \theta, p_r, p_\theta) = v p_\theta + \Vert p \Vert_{g}
-$$
+``
+    H(r, \\theta, p_r, p_\\theta) = v p_\\theta + \\Vert p \\Vert_{g}
+``
 
-where $v$ is a constant, $p = (p_r, p_\theta)$, and $\Vert \cdot \Vert_{g}$ is the norm induced by the metric
+where ``v`` is a constant, ``p = (p_r, p_\\theta)``, and ``\\Vert \\cdot \\Vert_{g}`` is the norm induced by the metric
 
-$$
-    g = \mathrm{d}r^2 + m_\lambda^2(r)\, \mathrm{d}\theta^2, \quad 
-    m_\lambda^2(r) = \frac{\sin^2 r}{1 - \lambda \sin^2 r}
-$$
+``
+    g = \\mathrm{d}r^2 + m_\\lambda^2(r)\\, \\mathrm{d}\\theta^2, \\quad 
+    m_\\lambda^2(r) = \\frac{\\sin^2 r}{1 - \\lambda \\sin^2 r}
+``
 
-with $\lambda = 4/5$.
+with ``\\lambda = 4/5``.
 
-Along the geodesics, we have $H+p^0 = 0$. The parameter $p^0$ is constant equal to $-1$ (hyperbolic), $0$ (abnormal) or $1$ (elliptic).
+Along the geodesics, we have ``H+p^0 = 0``. The parameter ``p^0`` is constant equal to ``-1`` (hyperbolic), ``0`` (abnormal) or ``1`` (elliptic).
 
-**Remark.** We can parameterize the geodesics by the norm of the initial convector, setting $\Vert{p_0}\Vert_g = 1$. 
-This amounts to parameterize by the initial angle $\alpha_0$:
-$$
-    p_r = \sin \alpha_0, \quad p_\theta = m_\lambda(r) \cos \alpha_0.
-$$
+**Remark.** We can parameterize the geodesics by the norm of the initial convector, setting ``\\Vert{p_0}\\Vert_g = 1``. 
+This amounts to parameterize by the initial angle ``\\alpha_0``:
+``
+    p_r = \\sin \\alpha_0, \\quad p_\\theta = m_\\lambda(r) \\cos \\alpha_0.
+``
 In that case, the hyperbolic geodeics are given by
-$$
-    p_\theta\, v + 1 = v\, m_\lambda(r) \cos \alpha_0 + 1 > 0.  
-$$
-```
\ No newline at end of file
+``
+    p_\\theta\\, v + 1 = v\\, m_\\lambda(r) \\cos \\alpha_0 + 1 > 0.  
+``
\ No newline at end of file