 
Summary: Dimensionality dierences between sticky and nonsticky
chaotic trajectory segments in a 3D Hamiltonian system
K. Tsiganis a,*, A. Anastasiadis b
, H. Varvoglis a
a
Section of Astrophysics, Astronomy and Mechanics, Department of Physics, University of Thessaloniki, GR540 06,
Thessaloniki, Greece
b
National Observatory of Athens, Institute for Space Applications and Remote Sensing, Palea Penteli, GR152 36, Greece
Accepted 28 July 1999
Abstract
Chaotic trajectories in Hamiltonian systems may have a peculiar evolution, owing to stickiness eects or migration to adjacent
stochastic regions. As a result, the function vt, which measures the exponential divergence of nearby trajectories, changes its be
haviour within dierent time intervals. We obtain such trajectories, through numerical integration, for a model 3D Hamiltonian
system. Having the plots of vt as a guide, we divide trajectories into segments, each one being assigned an Eective Lyapunov
Number (ELN), ki. We monitor the evolution of the trajectories through a ``quasiintegral'' time series, which can follow trapping or
escape events. Using the timedelay reconstruction scheme, we calculate the correlation dimension, D2
, of each trajectory segment.
Our numerical results show that, as the ELN of dierent segments increases, the correlation dimension of the set on which the tra
jectory segment is embedded, also tends to increase by a statistically signi®cant amount. This result holds only if the dierences of the
