Astronomy and Astrophysics – Astrophysics
Scientific paper
Jan 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995nyasa.773..168k&link_type=abstract
Waves in Astrophysics, vol. Volume 773, p. 168-188
Astronomy and Astrophysics
Astrophysics
Chaos, Nonlinear Systems, Time Dependence, Orbits, Periodic Functions, Orbital Mechanics, Orbit Perturbation, Hamiltonian Functions, Celestial Mechanics, Stochastic Processes, Liapunov Functions, Friction, Noise Spectra
Scientific paper
The authors are involved in the formulation of a new approach to the application of nonlinear dynamics to galactic dynamics, a theory of transient ensemble dynamics, which involves a consideration of the short time behavior of ensembles of orbits, restricting attention to astrophysically relevant timescales and eschewing longer time integrations except to the extent that they provide useful information about shorter time behavior. The simulations described in this paper lead to three potentially significantly conclusions: (1) Even very weak friction and noise, corresponding to a characteristic relaxation time as long as 106 - 109 t can have significant effects on both the pointwise and the statistical properties of orbits on short timescales less than 100 t, for example, by facilitating extrinsic diffusion through cantori. This would strongly suggest that realistic quasi equilibria must exhibit a detailed balance for transitions between different orbit classes. (2) One cannot necessarily conclude that resonant couplings are irrelevant for stochastic orbits. Indeed, because the Fourier spectra for such orbits are characterized by significant power for a broad range of frequencies, they will in general find it easier to couple to a generic disturbance than will regular orbits, which are characterized by only a relatively few frequencies. (3) Time-dependent modulation may trigger some diffusion through cantori. However, this effect seems substantially weaker than the extrinsic diffusion triggered by friction and noise, in the sense that the driving amplitude required to trigger substantial modulational diffusion is substantially larger in natural units than the friction amplitude required to trigger substantial modulational diffusion.
Abernathy Robert A.
Bradley Brendan O.
Kandrup Henry E.
Mahon Mary Elaine
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