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

This issue Previous Article Two dimensional histogram analysis using the Helmholtz principle Next Article Unique recovery of unknown projection orientations in three-dimensional tomography

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: March 31, 2008

Revised: July 31, 2008

Published: October 2008

Abstract Related Papers Cited by

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.

Citation:

Article Metrics

HTML views() PDF downloads(80) Cited by(0)

Dynamical tomography of gravitationally bound systems

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Dynamical tomography of gravitationally bound systems

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content