title: Analytic approach to bifurcation cascades in a class of generalized Hénon-Heiles potentials.
abstract: We investigate the bifurcation cascades of a linear librational orbit in a generalized class of Hénon-Heiles potentials. The stability traces of the new orbits created at its bifurcations are found numerically to intersect linearly at the saddle energy (e=1) , forming what we term the "Hénon-Heiles fans." In the limit close to the saddle energy (e-->1) , where the dynamics is nearly chaotic, we derive analytical asymptotic expressions for the stability traces of both types of orbits and confirm the numerically determined properties of the generalized Hénon-Heiles fans. As a bonus of our results, we obtain analytical approximations for the bifurcation energies e_{n} which become asymptotically exact for e_{n}-->1 .
authors.affiliation: Institute for Nuclear Research, 03680 Prospekt Nauki 47, Kiev, Ukraine.
authors.forename: Sergey N
authors.initials: SN
authors.lastname: Fedotkin
authors.forename: Alexander G
authors.initials: AG
authors.lastname: Magner
authors.forename: Matthias
authors.initials: M
authors.lastname: Brack