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There is a quite classical description of chaotic systems based on the behaviour of stable and unstable manifolds around a stationary point of the Poincaré section. It is presented, for example, [here, in slide 9][1], where a sketch of the stable and unstable manifolds on the Poincaré section are drawn by hand.

Now I am looking for a numerical study that reports the graphs of the stable and unstable manifolds, quantitatively evaluated (not just made by hand). Possibly, it should be done for Hénon-Heiles equations, or, alternatively, for another chaotic Hamiltonian system. It is important that it reports the conditions, i.e. the coordinates of the fixed point, so that I can exactly reproduce the calculation.

EDIT: I emphasize that I am looking for an example with the Henon-Heiles system. At least, with a Hamiltonian system. I see various examples with discrete maps, but there it is much easier to find a fixed point.

[1]: http://www.mat.uniroma2.it/~locatell/school1-astronet2/material/lezione_Loca1.pdf "KAM Theory and Applications in CelestialMechanics – First Lecture: Chaotic Motions in Hamiltonian Systems", Ugo Locatelli, University of Roma “Tor Vergata”, lecture, 14-th of January, 2013.

There is a quite classical description of chaotic systems based on the behaviour of stable and unstable manifolds around a stationary point of the Poincaré section. It is presented, for example, [here, in slide 9][1], where a sketch of the stable and unstable manifolds on the Poincaré section are drawn by hand.

Now I am looking for a numerical study that reports the graphs of the stable and unstable manifolds, quantitatively evaluated (not just made by hand). Possibly, it should be done for Hénon-Heiles equations, or, alternatively, for another chaotic Hamiltonian system. It is important that it reports the conditions, i.e. the coordinates of the fixed point, so that I can exactly reproduce the calculation.

EDIT: I emphasize that I am looking for an example with the Henon-Heiles system. At least, with a Hamiltonian system. I see various examples with discrete maps, but there it is much easier to find a fixed point.

EDIT 2. I could calculate the fixed point and the stable and unstable manifold but finding such a picture in an already published paper would help. Here is the reason. I am calculating some parameters in various points of the phase space. I represent them on the Poincarè section. I would like to qualitatively show how they behave near fixed points and stable and unstable manifolds. The topic of my paper would not be this comparison, nor the calculation of stable and unstable manifolds, thus I would like to refer the reader to a paper, without having to document the procedure of the calculation.

[1]: http://www.mat.uniroma2.it/~locatell/school1-astronet2/material/lezione_Loca1.pdf "KAM Theory and Applications in CelestialMechanics – First Lecture: Chaotic Motions in Hamiltonian Systems", Ugo Locatelli, University of Roma “Tor Vergata”, lecture, 14-th of January, 2013.

There is a quite classical description of chaotic systems based on the behaviour of stable and unstable manifolds around a stationary point of the Poincaré section. It is presented, for example, [here, in slide 9][1], where a sketch of the stable and unstable manifolds on the Poincaré section are drawn by hand.

Now I am looking for a numerical study that reports the graphs of the stable and unstable manifolds, quantitatively evaluated (not just made by hand). Possibly, it should be done for Hénon-Heiles equations, or, alternatively, for another chaotic Hamiltonian system. It is important that it reports the conditions, i.e. the coordinates of the fixed point, so that I can exactly reproduce the calculation.

[1]: http://www.mat.uniroma2.it/~locatell/school1-astronet2/material/lezione_Loca1.pdf "KAM Theory and Applications in CelestialMechanics – First Lecture: Chaotic Motions in Hamiltonian Systems", Ugo Locatelli, University of Roma “Tor Vergata”, lecture, 14-th of January, 2013.

There is a quite classical description of chaotic systems based on the behaviour of stable and unstable manifolds around a stationary point of the Poincaré section. It is presented, for example, [here, in slide 9][1], where a sketch of the stable and unstable manifolds on the Poincaré section are drawn by hand.

Now I am looking for a numerical study that reports the graphs of the stable and unstable manifolds, quantitatively evaluated (not just made by hand). Possibly, it should be done for Hénon-Heiles equations, or, alternatively, for another chaotic Hamiltonian system. It is important that it reports the conditions, i.e. the coordinates of the fixed point, so that I can exactly reproduce the calculation.

EDIT: I emphasize that I am looking for an example with the Henon-Heiles system. At least, with a Hamiltonian system. I see various examples with discrete maps, but there it is much easier to find a fixed point.

[1]: http://www.mat.uniroma2.it/~locatell/school1-astronet2/material/lezione_Loca1.pdf "KAM Theory and Applications in CelestialMechanics – First Lecture: Chaotic Motions in Hamiltonian Systems", Ugo Locatelli, University of Roma “Tor Vergata”, lecture, 14-th of January, 2013.

There is a quite classical description of chaotic systems based on the behaviour of stable and unstable manifolds around a stationary point of the Poincaré section. It is presented, for example, here, in slide 9, where a sketch of the stable and unstable manifolds on the Poincaré section are drawn by hand.

Now I am looking for a numerical study that reports the graphs of the stable and unstable manifolds, quantitatively evaluated (not just made by hand). Possibly, it should be done for Hénon-Heiles equations, or, alternatively, for another chaotic Hamiltonian system. It is important that it reports the conditions, i.e. the coordinates of the fixed point, so that I can exactly reproduce the calculation.

There is a quite classical description of chaotic systems based on the behaviour of stable and unstable manifolds around a stationary point of the Poincaré section. It is presented, for example, [here, in slide 9][1], where a sketch of the stable and unstable manifolds on the Poincaré section are drawn by hand.

Now I am looking for a numerical study that reports the graphs of the stable and unstable manifolds, quantitatively evaluated (not just made by hand). Possibly, it should be done for Hénon-Heiles equations, or, alternatively, for another chaotic Hamiltonian system. It is important that it reports the conditions, i.e. the coordinates of the fixed point, so that I can exactly reproduce the calculation.

[1]: http://www.mat.uniroma2.it/~locatell/school1-astronet2/material/lezione_Loca1.pdf "KAM Theory and Applications in CelestialMechanics – First Lecture: Chaotic Motions in Hamiltonian Systems", Ugo Locatelli, University of Roma “Tor Vergata”, lecture, 14-th of January, 2013.