Occurrence of periodic Lamé functions at bifurcations in chaotic Hamiltonian systems

Details Occurrence of periodic Lamé functions at bifurcations in chaotic Hamiltonian systems Occurrence of periodic Lamé functions at bifurcations in chaotic Hamiltonian systems

2001-05-22

arxiv.org/abs/nlin/0105048v3

Journal of Physics A 34, 8199 (2001)

Nonlinear Sciences

Chaotic Dynamics

LaTeX2e, 22 pages, 14 figures. Version 3: final form of paper, accepted by J. Phys. A. Changes in Table 2; new reference [25];

Scientific paper

10.1088/0305-4470/34/40/301

We investigate cascades of isochronous pitchfork bifurcations of straight-line librating orbits in some two-dimensional Hamiltonian systems with mixed phase space. We show that the new bifurcated orbits, which are responsible for the onset of chaos, are given analytically by the periodic solutions of the Lam\'e equation as classified in 1940 by Ince. In Hamiltonians with C_${2v}$ symmetry, they occur alternatingly as Lam\'e functions of period 2K and 4K, respectively, where 4K is the period of the Jacobi elliptic function appearing in the Lam\'e equation. We also show that the two pairs of orbits created at period-doubling bifurcations of touch-and-go type are given by two different linear combinations of algebraic Lam\'e functions with period 8K.

Affiliated with

Also associated with

No associations

Rating

Occurrence of periodic Lamé functions at bifurcations in chaotic Hamiltonian systems 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 Occurrence of periodic Lamé functions at bifurcations in chaotic Hamiltonian systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Occurrence of periodic Lamé functions at bifurcations in chaotic Hamiltonian systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-354173