| 11. | Equivalently, it is a manifold that is ( if connected ) monodromy acting by affine transformations.
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| 12. | A change of basepoint merely results in a ( simultaneous ) conjugation of all the monodromy matrices.
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| 13. | In particular, many of these self-similar groups arise as iterated monodromy groups of complex polynomials.
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| 14. | However, if the monodromy is nontrivial, there is no such gauge transformation for the whole outside region.
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| 15. | Iterated monodromy groups of rational functions usually have exotic properties from the point of view of classical group theory.
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| 16. | This is called the "'monodromy theorem "'and its statement is made precise below.
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| 17. | The proof of the existence of such differential equations by previously known monodromy matrices is one of the Hilbert problems.
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| 18. | This Chekanov-Eliashberg invariant yields an invariant for loops of Legendrian knots by considering the monodromy of the loops.
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| 19. | The monodromy matrices modulo simultaneous conjugation define the "'monodromy data "'of the Fuchsian system.
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| 20. | The monodromy matrices modulo simultaneous conjugation define the "'monodromy data "'of the Fuchsian system.
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