Box dimension of trajectories of some discrete dynamical systems

Neven Elezović, Vesna Županović and Darko Žubrinić

Chaos, Solitons & Fractals, 2007, vol. 34, issue 2, 244-252

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.

Date: 2007
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:34:y:2007:i:2:p:244-252

DOI: 10.1016/j.chaos.2006.03.060

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