We derive stability traces of bifurcating orbits in H\'enon-Heiles potentials
near their saddlesComment: LaTeX revtex4, 38 pages, 7 PostScript figures, 2 table

A. Erdélyi

A. M. Ozorio de Almeida

A. P. Prudnikov

Alexander G. Magner

E. L. Ince

I. S. Gradshteyn

M. Brack

M. C. Gutzwiller

M. V. Fedoryuk

Matthias Brack

R. C. Churchill

Sergey N. Fedotkin

W. Magnus

English

arXiv

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 chaotic, we derive analytical asymptotic expressions for the stability traces of both types of orbits  and confirm the numerically determined properties of the generalized ``H\'enon-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

Fedotkin, S.

Magner, A.

Brack, Matthias

University of Regensburg Publication Server

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

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https://epub.uni-regensburg.de/7819/1/PhysRevE.77.066219.pdf

Analytic approach to bifurcation cascades in a class of generalized
  H\'enon-Heiles potentials

Analytic approach to bifurcation cascades in a class of generalized H\'enon-Heiles potentials

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University of Regensburg Publication Server

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