Geodesic
Creating transverse homoclinic connections in planar billiards
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 122-134

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Given a planar billiard system containing stable and unstable manifolds that intersect non-transversely, we show how to make a local perturbation to the boundary that causes the intersection to become transverse. We apply these ideas to billiards inside an ellipse. 
@article{ZNSL_2003_300_a10,
     author = {V. J. Donnay},
     title = {Creating transverse homoclinic connections in planar billiards},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {122--134},
     publisher = {mathdoc},
     volume = {300},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a10/}
}
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V. J. Donnay. Creating transverse homoclinic connections in planar billiards. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 122-134. http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a10/