A solution of the problem of reconstructing a mathematical model using
statistical methods to specify the evolution operator is optimized. I
t is shown that this procedure can be used for modeling with short tim
e series, so that the metric and dynamic characteristics of an attract
or can be determined with a knowledge of the reconstructed model equat
ions. Direct methods of analyzing scalar time series are less effectiv
e in this situation. (C) 1997 American Institute of Physics. [S1063-78
50(97)01804-1].