We study Khintchine's conjecture : The sequence of partial 
quotients in the continued fraction expansions of algebraic numbers (degree 
≧ 3) is random and unbounded.  Our purpose is to show that the asymptotic 
behavior of these partial quotients is unpredictable by proving that the 
gap value of recurrent dimensions is positive, or chaotic by proving that 
its topological entropy is positive.
 Here we give the following partial results : For some transcendental 
numbers the topological entropies　
and the recurrent dimensions of the sequences of their partial quotients 
are zero.