Detecting Singularities Using the PowerSeries Library

  • Mahsa KazemiEmail author
  • Marc Moreno Maza
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1125)


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.


Singularities Smooth maps Lyapunov-Schmidt reduction Extended Hensel Construction PowerSeries library 


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of Western OntarioLondonCanada

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