Box dimension of trajectories of some discrete dynamical systems
Dynamical Systems
2009-10-28 v1
Abstract
We study the asymptotics, box dimension, and Minkowski content of trajectories of some discrete dynamical systems. We show that under very general conditions, trajectories corresponding to parameters where saddle-node bifurcation appears have box dimension equal to 1/2, while those corresponding to period-doubling bifurcation parameter have box dimension equal to 2/3. Furthermore, all these trajectories are Minkowski nondegenerate. The results are illustrated in the case of logistic map.
Keywords
Cite
@article{arxiv.0910.4999,
title = {Box dimension of trajectories of some discrete dynamical systems},
author = {Neven Elezović and Vesna Županović and Darko Žubrinić},
journal= {arXiv preprint arXiv:0910.4999},
year = {2009}
}
Comments
12 pages