Abstract
We consider a class of unfoldings of quasi-regular functions. We assume that such perturbations have asymptotic developments which depend on many unfoldings of the logarithm function. We prove a preparation theorem for such functions; namely, they are “conjugated” to a finite principal part via a “pseudo-isomorphism”. This finite principal part is polynomial in the phase variable and these unfoldings of the logarithm function. As an application there exists a uniform bound in the parameter of the numbers of zeros of such class of non-differentiable functions. A finiteness result of the number of the limit cycles bifurcating from a perturbed hyperbolic polycycle is obtained too.
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Morsalani, M.E., Mourtada, A. (2016). A Preparation Theorem for a Class of Non-differentiable Functions with an Application to Hilbert’s 16th Problem. In: Toni, B. (eds) Mathematical Sciences with Multidisciplinary Applications. Springer Proceedings in Mathematics & Statistics, vol 157. Springer, Cham. https://doi.org/10.1007/978-3-319-31323-8_8
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DOI: https://doi.org/10.1007/978-3-319-31323-8_8
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