Analytic approach to bifurcation cascades in a class of generalized Hénon-Heiles potentials

URN to cite this document:: urn:nbn:de:bvb:355-epub-78198
DOI to cite this document:: 10.5283/epub.7819

Fedotkin, S. ; Magner, A. ; Brack, Matthias

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Date of publication of this fulltext: 05 Aug 2009 13:57

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Abstract

We investigate the bifurcation cascades of a linear librational orbit in a generalized class of H\'enon-Heiles potentials. The stability traces of the new orbits born at its bifurcations are found numerically to intersect linearly at the saddle energy (e=1), forming what we term the ``H\'enon-Heiles fans''. In the limit close to the saddle energy (e-->1), where the dynamics is nearly ...