ELA, Volume 15, pp. 22-49, January 2006, abstract.

Bounded and stably bounded palindromic difference 
equations of first order

Leiba Rodman

Criteria for palindromic difference equations A*x_i + Ax_(i+1)=0,
where * stands for either transpose or conjugate transpose, to  
have bounded or stably bounded solutions are given in terms 
of the congruent equivalent classes of the matrix A. It is proved
that the set of bounded palindromic difference equations is 
connected in the complex case, and has two connected components 
corresponding to the sign of the determinant of A in the real case. 
The connected components of the set of stably bounded palindromic 
difference equations are characterized.