Effective algebraic geometry and normal forms of reversible mappings
The authors consider a problem coming from the theory of discrete dynamical systems (iterations of diffeomorphisms in \({\mathbb R}^3\)). Namely, how to characterize the behaviour of the trajectories near the fixed points and the stability of this behaviour under perturbations. The authors use the computer in the context of reversible mappings. When such a mapping has some degree of degeneracy they apply Gröbner bases techniques and the theory of (formal) normal forms in the space of the coefficients of the jets of the mapping. They show that a language with typed objects like AXIOM is very convenient to solve such problems.
scientific article; zbMATH DE number 1808648