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November  2008, 2(4): 527-546. doi: 10.3934/ipi.2008.2.527

Dynamical tomography of gravitationally bound systems

Mikko Kaasalainen 1,

1. 

Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FI-00014, Finland

Received  April 2008 Revised  August 2008 Published  November 2008

We study the inverse problem of deducing the dynamical characteristics (such as the potential field) of large systems from kinematic observations. We show that, for a class of steady-state systems, the solution is unique even with fragmentary data, dark matter, or selection (bias) functions. Using spherically symmetric models for simulations, we investigate solution convergence and the roles of data noise and regularization in the inverse problem. We also present a method, analogous to tomography, for comparing the observed data with a model probability distribution such that the latter can be determined.
Keywords: $n$-body problems, Quasi-periodic motions and invariant tori, Mathematical physics, Inverse problems, Dynamical systems, Hamiltonian systems, Galactic and stellar dynamics.
Mathematics Subject Classification: 35Q72, 37J(35,40), 49N45, 65C05, 70[F(10,17), H(06,08,33), K43], 85A05.
Citation: Mikko Kaasalainen. Dynamical tomography of gravitationally bound systems. Inverse Problems & Imaging, 2008, 2 (4) : 527-546. doi: 10.3934/ipi.2008.2.527
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