Pandas: Finding maxima of 2d data (integers) in Dataframe

I have a 2d data set of (x,y). x and y are integer values.

How can I use only Pandas code to find all x values where y reaches its maximum values (there are multiple and same absolute maxima)?

I also want to plot (with pandas.DataFrame.plot) x vs. y and mark the maxima positions.

Example code:

import numpy as np
import pandas as pd

np.random.seed(10)

x = np.arange(100)*0.2
y = np.random.randint(0, 20, size=100)

data = np.vstack((x, y)).T

df = pd.DataFrame(data, columns=['x', 'y'])

ymax = df['y'].max()

df_ymax = df[df['y'] == ymax]

print(df_ymax)

#        x     y
# 13   2.6  19.0
# 24   4.8  19.0
# 28   5.6  19.0
# 86  17.2  19.0
# 88  17.6  19.0

df.plot(x='x', y='y', figsize=(8, 4),
        ylabel='y', legend=False, style=['b-'])

I have no idea how to mark the maxima values (df_ymax) in the same plot, e.g. using circles. How can that be solved?

The final plot should look like this (here I programmed everything with numpy and matplotlib):

>Solution :

Get the Axes returned by df.plot and reuse it to plot the maxima values:

ax = df.plot(x='x', y='y', figsize=(8, 4), ylabel='y', legend=False, style=['b-'])
df_ymax.plot.scatter(x='x', y='y', color='r', ax=ax)