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| Systems of difference equations defined by linear fractionals sharing denominator are studied. Such systems can be nicely described in terms of a square matrix by the use of homogeneous coordinates. The talk will focus on the existence of invariant affine varieties and quadrics. In particular, we show that there is a correspondence between invariant non-degenerate quadrics and solutions to certain matrix equation involving the matrix defining the system. Further, when such matrix is semisimple, it is proved that every orbit is contained either in an invariant affine variety or in an invariant quadric. |
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