Dynamical tomography of gravitationally bound systems

Mikko Kaasalainen

doi:10.3934/ipi.2008.2.527

Article Contents

2008, Volume 2, Issue 4: 527-546. Doi: 10.3934/ipi.2008.2.527

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Dynamical tomography of gravitationally bound systems

Mikko Kaasalainen^1,

1.
Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FI-00014

Received: April 2008

Revised: August 2008

Published: November 2008

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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.

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