An algorithm for symbolic computation of center manifolds

  • Emilio Freire
  • Estanislao Gamero
  • Enrique Ponce
  • Leopoldo G. Franquelo
Differential Equations
Part of the Lecture Notes in Computer Science book series (LNCS, volume 358)


A useful technique for the study of local bifurcations is the center manifold theory because a dimensional reduction is achieved. The computation of Taylor series approximations of center manifolds gives rise to several difficulties regarding the operational complexity and the computational effort. Previous works proceed in such a way that the computational effort is not optimized. In this paper an algorithm for center manifolds well suited to symbolic computation is presented. The algorithm is organized according to an iterative scheme making good use of the previous steps, thereby minimizing the number of operations. The results of two examples obtained through a REDUCE 3.2 implementation of the algorithm are included.


Normal Form Homogeneous Polynomial Computer Algebra Symbolic Computation Center Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Emilio Freire
    • 1
  • Estanislao Gamero
    • 1
  • Enrique Ponce
    • 1
  • Leopoldo G. Franquelo
    • 2
  1. 1.Department of Applied MathematicsEscuela Superior Ingenieros IndustrialesSevillaSpain
  2. 2.Department of Electronic Engineering, Systems and AutomaticsEscuela Superior Ingenieros IndustrialesSevillaSpain

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