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    Extension of formal conjugations between diffeomorphisms

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    We study the formal conjugacy properties of germs of complex analytic diffeomorphisms defined in the neighborhood of the origin of Cn{\mathbb C}^{n}. More precisely, we are interested on the nature of formal conjugations along the fixed points set. We prove that there are formally conjugated local diffeomorphisms ϕ,η\phi, \eta such that every formal conjugation σ^\hat{\sigma} (i.e. ησ^=σ^ϕ\eta \circ \hat{\sigma} = \hat{\sigma} \circ \phi) does not extend to the fixed points set Fix(ϕ)Fix (\phi) of ϕ\phi, meaning that it is not transversally formal (or semi-convergent) along Fix(ϕ)Fix (\phi). We focus on unfoldings of 1-dimensional tangent to the identity diffeomorphisms. We identify the geometrical configurations preventing formal conjugations to extend to the fixed points set: roughly speaking, either the unperturbed fiber is singular or generic fibers contain multiple fixed points.Comment: 34 page

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    Mittag-Leffler Functions with Three Parameters

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    Introduction

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    Historical Overview of the Mittag-Leffler Functions

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    Applications to Fractional Order Equations

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