Hattori T.
Asymptotically one-dimensional diffusions on scale-irregular gaskets.
(94K, LaTeX Version 2.09 <3 Jan 1988>)

ABSTRACT.  A simple class of fractals which lack exact self-similarity is introduced, 
and the asymptotically one-dimensional diffusion process is constructed.
The process moves mostly horizontally for very small scales, while for large 
scales it diffuses almost isotropically, in the sense of the off-horizontal 
relative jump rate for the decimated random walks of the process.
An essential step in the construction of diffusion is to prove the existence 
of appropriate time-scaling factors.  For this purpose, a limit theorem for 
a discrete-time multi-type supercritical branching processes with 
singular and irregular (varying) environment, is developed.