On the Asymptotics of the Hopf Characteristic Function

Details On the Asymptotics of the Hopf Characteristic Function On the Asymptotics of the Hopf Characteristic Function

2012-01-13

arxiv.org/abs/1201.2793v1

Nonlinear Sciences

Chaotic Dynamics

13 pages, 2 figures

Scientific paper

We study the asymptotic behavior of the Hopf characteristic function for some well known fractals and chaotic dynamical systems. The relationship between asymptotics and fractional dimension is reviewed. In the case of a natural measure on the generalized Cantor set, we show that the asymptotics saturates a bound arising from theorems about the s-capactity. We consider some well known chaotic dynamical systems numerically, for which crude estimates for the asymptotics are consistent with the known Hausdorff dimension.

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