1998/10/06 by Henry E. Kandrup, John Drury, JOHN DRURY
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Chaotic #Chaotic systems #Classical mechanics #Computer science #Cosmology and Gravitation Theories #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear system #Orbit (dynamics) #Periodic orbits #Perturbation (astronomy) #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Spectral line #Statistical physics #astro-ph
paper · pdf · doi:10.1111/j.1749-6632.1998.tb11266.x
16 pages LaTeX, including 5 figures, no macros required
arxiv created 1998/10/06 · openalex publication_date 1998/12/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
This paper summarizes a numerical investigation which aimed to identify and characterize regular and chaotic behavior in time-dependent Hamiltonians H(r, p, t) = p(2)/2 + V(r, t), with V = R(t)V0(r) or V = V0[R(t)r], where V0 is a polynomial in x, y, and/or z and R(t) proportional to tP is a time-dependent scale factor. When p is not too negative, one can distinguish between regular and chaotic behavior by determining whether an orbit segment exhibits a sensitive dependence on initial conditions. However, chaotic segments in these potentials differ from chaotic segments in time-independent potentials in that a small initial perturbation will usually exhibit a sub- or superexponential growth in time. Although not periodic, regular segments typically exhibit simpler shapes, topologies, and Fourier spectra than do chaotic segments. This distinction between regular and chaotic behavior is not absolute since a single orbit segment can seemingly change from regular to chaotic and vice versa. All these observed phenomena can be understood in terms of a simple theoretical model.