Computer Algebra Methods for Equivariant Dynamical Systems

This book starts with an overview of the research of Gröbner bases which have many applications in various areas of mathematics since they are a general tool for the investigation of polynomial systems. The next chapter describes algorithms in invariant theory including many examples and time table...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριος συγγραφέας: Gatermann, Karin (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2000.
Έκδοση:1st ed. 2000.
Σειρά:Lecture Notes in Mathematics, 1728
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
Πίνακας περιεχομένων:
  • Gröbner bases: Buchberger's algorithm
  • The consequence of grading
  • Definitions and the relation to Gröbner bases
  • Computation of a Hilbert series
  • The Hilbert series driven Buchberger algorithm
  • The computation with algebraic extensions
  • Detection of Gröbner bases
  • Dynamic Buchberger algorithm
  • Elimination
  • Algorithms of the computation of invariants and equivariants: Using the Hilbert series
  • Invariants
  • Equivariants
  • Using the nullcone
  • Using a homogeneous system of parameters
  • Computing uniqueness
  • Symmetric bifurcation theory
  • Local bifurcation analysis
  • An example of secondary Hopf bifurcation
  • Orbit space reduction
  • Exact computation of steady states
  • Differential equations on the orbit space
  • Using Noether normalization
  • Further reading
  • References
  • Index.