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

.. only:: html

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

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

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

.. _sphx_glr_matplotlib_plot_mset_henon.py:


mset of the Henon map
==========================

[1]A. Shudo and K. S. Ikeda, Complex Trajectory Description for Chaotic Tunneling, Progress of Theoretical Physics Supplement 139, 246 (2000).

.. GENERATED FROM PYTHON SOURCE LINES 9-78



.. image:: /matplotlib/images/sphx_glr_plot_mset_henon_001.png
    :alt: plot mset henon
    :class: sphx-glr-single-img





.. code-block:: default


    import numpy as np
    import matplotlib.pyplot as plt

    import warnings
    warnings.filterwarnings('ignore')

    #np.seterr(invalid='ignore')

    twopi = 2*np.pi

    def get_Mset(evolve, pinit, tmax, xr=[0,twopi], yr =[-3,3],sample=500):
        qr = np.linspace(xr[0], xr[1], sample)
        qi = np.linspace(yr[0], yr[1], sample)
        if yr[0]*yr[1]<0:
            qi = np.linspace(yr[0], 0, sample//2,endpoint=False)
            qi = np.append(qi, np.linspace(0, yr[1], sample//2))

        QR,QI = np.meshgrid(qr,qi)
        q0 = QR + 1.j*QI
        p0 = np.zeros(q0.shape, dtype=np.complex128) + pinit
        x = np.array([np.copy(q0), np.copy(p0)])
        initial = np.copy(q0)

        x = evolves(x, tmax, evolve)
        index = (np.abs(x[0]) > 1e100) & (np.abs(x[1]) > 1e100)
        #x[0][index] = np.nan + 1.j*np.nan
        #x[1][index] = np.nan + 1.j*np.nan
        x[0][index] = np.inf
        x[1][index] = np.inf
        prod = x[1].imag*np.roll(x[1].imag,1)
        index = (prod > 0)
        return [initial, q0[~index], x]

    def plot_contour(ax,levels, init, lset):
        #vmax = lset[1][~np.isnan(lset[1])].imag.max()
        ax.contour(init.real, init.imag, lset[1].imag, levels, colors='k',alpha=0.5,lw=1)



    def fmap(x, c):
        q,p = x
        p = p - (c  - q**2)
        q = q + p #+ np.sin(p)
        return np.array([q, p])

    def evolves(x, tmax, evolve):
        for i in range(tmax):
            x = evolve(x)
        return x

    tmax = 6
    c=0.8
    evolve = lambda x: fmap(x, c)
    init, mset, lset = get_Mset(evolve, 0, tmax, sample=2000, xr=[-2,2], yr=[-2,2])
    fig, ax = plt.subplots(1,1)
    ax.plot(mset.real, mset.imag, ',k')

    levels = np.linspace(-2,2,20)
    plot_contour(ax, levels, init, lset)

    levels = [-np.inf, 0, np.inf]
    colors = ["#00ff7f", "#00ffff"]
    ax.contour(init.real, init.imag, lset[1].imag, levels, colors='k',linewidths=1)
    ax.contourf(init.real, init.imag, lset[1].imag, levels, colors=colors,alpha=0.5, linewidths=3)

    ax.set_xlabel(r"$\mathrm{Re}[x_0]$")
    ax.set_ylabel(r"$\mathrm{Im}[x_0]$")
    plt.show()


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

   **Total running time of the script:** ( 0 minutes  1.905 seconds)


.. _sphx_glr_download_matplotlib_plot_mset_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_mset_henon.py <plot_mset_henon.py>`



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

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


.. only:: html

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

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