*Astron. Astrophys. 317, 73-81 (1997)*
## A fast method for distinguishing between ordered
and chaotic orbits
**
G. Contopoulos and
N. Voglis
**
Department of Astronomy, University of Athens
Panepistimiopolis, GR-15784 Athens, Greece
*Received 14 February 1996 / Accepted 17 May 1996*
**Abstract**
We describe a new method of distinguishing between ordered and
chaotic orbits, which is much faster than the methods used up to now,
namely (1) the distribution of the Poincaré consequents, (2)
the Lyapunov characteristic number and (3) the distribution of the
rotation angles. This method is based on the distribution of the
helicity angles (the angles of small deviations
from a given orbit with a fixed direction), or
of the twist angles (the differences of successive helicity angles),
and the stretching numbers (the logarithms of the ratios of successive
deviations
, also called 'short time Lyapunov characteristic
numbers'). We apply this method to 2-D mappings and 4-D mappings,
representing Hamiltonian systems of 2 and 3 degrees of freedom
respectively.
**Key words:** chaos
stellar
dynamics
Galaxy: kinematics and dynamics
Send offprint requests to: G. Contopoulos
### Contents
© European Southern Observatory (ESO) 1997
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