Analytic approach to bifurcation cascades in a class of generalized H\'enon-Heiles potentials
S. N. Fedotkin (1), A. G. Magner (1), M. Brack (2) ((1) Institute for, Nuclear Research, Kiev, Ukraine, (2) Institut f\"ur Theoretische Physik,, Universit\"at Regensburg, Regensburg, Germany)
TL;DR
This paper develops an analytical method to study bifurcation cascades in generalized Hénon-Heiles potentials by deriving stability traces of bifurcating orbits near saddle points.
Contribution
It introduces an analytical approach to compute stability traces of bifurcating orbits in a class of generalized Hénon-Heiles potentials.
Findings
Derived stability traces for bifurcating orbits near saddles.
Provided insights into bifurcation cascades in Hénon-Heiles systems.
Enhanced understanding of orbit stability in nonlinear potentials.
Abstract
We derive stability traces of bifurcating orbits in H\'enon-Heiles potentials near their saddles
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