Bifurcation Cascades and Self-Similarity of Periodic Orbits with Analytical Scaling Constants in Hénon–Heiles Type Potentials View Full Text


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Article Info

DATE

2001-02

AUTHORS

Matthias Brack

ABSTRACT

We investigate the isochronous bifurcations of the straight-line librating orbit in the Hénon–Heiles and related potentials. With increasing scaled energy e, they form a cascade of pitchfork bifurcations that cumulate at the critical saddle-point energy e=1. The stable and unstable orbits created at these bifurcations appear in two sequences whose self-similar properties possess an analytical scaling behavior. Different from the standard Feigenbaum scenario in area preserving two-dimensional maps, here the scaling constants α and β corresponding to the two spatial directions are identical and equal to the root of the scaling constant δ that describes the geometric progression of bifurcation energies en in the limit n→∞. The value of δ is given analytically in terms of the potential parameters. More... »

PAGES

209-232

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Identifiers

URI

http://scigraph.springernature.com/pub.10.1023/a:1017582218587

DOI

http://dx.doi.org/10.1023/a:1017582218587

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1000516379


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