Inverse Problems and Imaging (IPI)

Dynamical tomography of gravitationally bound systems

Pages: 527 - 546, Volume 2, Issue 4, November 2008      doi:10.3934/ipi.2008.2.527

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Mikko Kaasalainen - Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FI-00014, Finland (email)

Abstract: 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:  Inverse problems, Mathematical physics, Dynamical systems, Hamiltonian systems, Quasi-periodic motions and invariant tori, $n$-body problems, Galactic and stellar dynamics
Mathematics Subject Classification:  35Q72, 37J(35,40), 49N45, 65C05, 70[F(10,17), H(06,08,33), K43], 85A05

Received: April 2008;      Revised: August 2008;      Available Online: November 2008.