Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2000-06-21
Foundations of Physics 31, 209-232 (2001)
Nonlinear Sciences
Chaotic Dynamics
20 pages, 10 figures, LaTeX. Contribution to Festschrift "To Martin C. Gutzwiller on His Seventy-Fifth Birthday", eds. A. Inom
Scientific paper
We investigate the isochronous bifurcations of the straight-line librating orbit in the Henon-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 \alpha and \beta corresponding to the two spatial directions are identical and equal to the root of the scaling constant \delta that describes the geometric progression of bifurcation energies e_n in the limit n --> infinity. The value of \delta is given analytically in terms of the potential parameters.
No associations
LandOfFree
Bifurcation cascades and self-similarity of periodic orbits with analytical scaling constants in Henon-Heiles type potentials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Bifurcation cascades and self-similarity of periodic orbits with analytical scaling constants in Henon-Heiles type potentials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bifurcation cascades and self-similarity of periodic orbits with analytical scaling constants in Henon-Heiles type potentials will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-23061