Abrupt bifurcations in chaotic scattering: view from the anti-integrable limit

Claude Baesens, Yi-Chiuan Chen, Robert S MacKay
2013 Nonlinearity  
Bleher, Ott and Grebogi found numerically an interesting chaotic phenomenon in 1989 for the scattering of a particle in a plane from a potential field with several peaks of equal height. They claimed that when the energy E of the particle is slightly less than the peak height E c there is a hyperbolic suspension of a topological Markov chain from which chaotic scattering occurs, whereas for E > E c there are no bounded orbits. They called the bifurcation at E = E c an abrupt bifurcation to
more » ... bifurcation to chaotic scattering. The aim of this paper is to establish a rigorous mathematical explanation for how chaotic orbits occur via the bifurcation, from the viewpoint of the antiintegrable limit, and to do so for a general range of chaotic scattering problems.
doi:10.1088/0951-7715/26/9/2703 fatcat:kcsazbdk2vf4tmwj2tubw77zcm