.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "matplotlib/plot_henon.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_matplotlib_plot_henon.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_matplotlib_plot_henon.py:


area-preserving Hénon map
========= 

.. math::

    p_{n+1} &= p_{n} - V'(q_{n}) \\
    q_{n+1} &= q_{n} + p_{n}

where :math:`V(q) = cq + q^3/3`

.. GENERATED FROM PYTHON SOURCE LINES 13-43



.. image:: /matplotlib/images/sphx_glr_plot_henon_001.png
    :alt: plot henon
    :class: sphx-glr-single-img





.. code-block:: default


    import numpy as np
    import matplotlib.pyplot as plt

    import warnings
    warnings.filterwarnings('ignore')


    def fmap(q,p,c):
        p = p - (c - q**2)
        q = q + p
        return q, p

    tmax = 1000
    sample=1000
    c = 0.8
    q = np.linspace(-5,5,sample)
    p = np.array([0.0]*sample)
    traj = [np.array([])]*2
    for i in range(tmax):
        q,p = fmap(q,p,c)
    
    
        traj[0] = np.append(traj[0], q)
        traj[1] = np.append(traj[1], p)    

    fig, ax = plt.subplots(1,1)
    ax.plot(traj[0], traj[1], ",k")
    ax.set_xlim(-2,2)
    ax.set_ylim(-2,2)
    plt.show()

.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  0.581 seconds)


.. _sphx_glr_download_matplotlib_plot_henon.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example



  .. container:: sphx-glr-download sphx-glr-download-python

     :download:`Download Python source code: plot_henon.py <plot_henon.py>`



  .. container:: sphx-glr-download sphx-glr-download-jupyter

     :download:`Download Jupyter notebook: plot_henon.ipynb <plot_henon.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_