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**Topological equivalence and structural stability for linear difference equations.**
*(English)*
Zbl 0753.34040

Summary: In this paper first we prove that if two linear difference equations with invertible coefficient matrices are topologically equivalent and one of them has bounded coefficient matrix together with its inverse, then the coefficient matrix of the other equation is also bounded together with its inverse. We also prove that if a linear difference equation with bounded and invertible coefficient matrix is structurally stable then the inverse of the coefficient matrix is also bounded.

### MSC:

34D30 | Structural stability and analogous concepts of solutions to ordinary differential equations |

34A30 | Linear ordinary differential equations and systems |

39A11 | Stability of difference equations (MSC2000) |

### Keywords:

topological equivalence; structural stability; linear difference equations; bounded coefficient matrix
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\textit{J. Kurzweil} and \textit{G. Papaschinopoulos}, J. Differ. Equations 89, No. 1, 89--94 (1991; Zbl 0753.34040)

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### References:

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