Abstract
Local bifurcation analysis of singular smooth maps plays a fundamental role in understanding the dynamics of real world problems. This analysis is accomplished in two steps: first performing the Lyapunov-Schmidt reduction to reduce the dimension of the state variables in the original smooth map and then applying singularity theory techniques to the resulting reduced smooth map. In this paper, we address an important application of the so-called Extended Hensel Construction (EHC) for computing the aforementioned reduced smooth map, which, consequently, leads to detecting the type of singularities of the original smooth map. Our approach is illustrated via two examples displaying pitchfork and winged cusp bifurcations.
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Notes
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The factorization based on Hensel Lemma is in fact a weaker construction since: (1) the input polynomial must be monic and (2) the output factors may not be linear.
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Kazemi, M., Moreno Maza, M. (2020). Detecting Singularities Using the PowerSeries Library. In: Gerhard, J., Kotsireas, I. (eds) Maple in Mathematics Education and Research. MC 2019. Communications in Computer and Information Science, vol 1125. Springer, Cham. https://doi.org/10.1007/978-3-030-41258-6_11
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