We study large deviations for Brownian motion on the Sierpinski gasket in t
he short time limit. Because of the subtle oscillation of hitting times of
the process, no large deviation principle can hold. In fact, our result sho
ws that there is an infinity of different large deviation principles for di
fferent subsequences, with different (good) rate functions. Thus, instead o
f taking the time scaling epsilon --> 0, we prove that the large deviations
hold for E-n(z) = (2/5)(n)z as n --> infinity, using one parameter family
of rate functions I-z (z is an element of [2/5, 1)). As a corollary, we obt
ain Strassen-type laws of the iterated logarithm. (C) 2000 Elsevier Science
B.V. All rights reserved. MSG. 60F10; 60J60; 60J80.