How to add a second x-axis in matplotlib

I’m taking a cue from the comments in @Dhara’s answer, it sounds like you want to set a list of new_tick_locations by a function from the old x-axis to the new x-axis. The tick_function below takes in a numpy array of points, maps them to a new value and formats them:

import numpy as np
import matplotlib.pyplot as plt

fig = plt.figure()
ax1 = fig.add_subplot(111)
ax2 = ax1.twiny()

X = np.linspace(0,1,1000)
Y = np.cos(X*20)

ax1.plot(X,Y)
ax1.set_xlabel(r"Original x-axis: $X$")

new_tick_locations = np.array([.2, .5, .9])

def tick_function(X):
    V = 1/(1+X)
    return ["%.3f" % z for z in V]

ax2.set_xlim(ax1.get_xlim())
ax2.set_xticks(new_tick_locations)
ax2.set_xticklabels(tick_function(new_tick_locations))
ax2.set_xlabel(r"Modified x-axis: $1/(1+X)$")
plt.show()