info prev up next book cdrom email home

Pointwise Dimension


\begin{displaymath}
D_P({\bf x}) \equiv \lim_{\epsilon\to 0} {\ln \mu(B_\epsilon({\bf x}))\over \ln\epsilon},
\end{displaymath}

where $B_\epsilon({\bf x})$ is an $n$-D Ball of Radius $\epsilon$ centered at ${\bf x}$ and $\mu$ is the Probability Measure.

See also Ball, Probability Measure


References

Nayfeh, A. H. and Balachandran, B. Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods. New York: Wiley, pp. 541-545, 1995.




© 1996-9 Eric W. Weisstein
1999-05-25