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Criteria for palindromic difference equations A*xi + Axi+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.