Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
Dimensionality dierences between sticky and non-sticky chaotic trajectory segments in a 3D Hamiltonian system
 

Summary: Dimensionality dierences between sticky and non-sticky
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, GR-540 06,
Thessaloniki, Greece
b
National Observatory of Athens, Institute for Space Applications and Remote Sensing, Palea Penteli, GR-152 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 ``quasi-integral'' time series, which can follow trapping or
escape events. Using the time-delay 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

  

Source: Anastasiadis, Anastasios - Institute for Space Applications and Remote Sensing, National Observatory of Athens
Varvoglis, Harry - Department of Physics, Aristotle University of Thessaloniki

 

Collections: Physics