Depot des Theses - Algorithms for locally nilpotent derivations in dimension two and three

Derivations, especially locally nilpotent ones, over polynomial rings are objects of great importance in many ﬁelds of pure and applied mathematics. Nowadays, locally nilpotent derivations have made remarkable progress and became an important topic in understanding affine algebraic geometry and commutative algebra. This is due to the fact that some classic problems in these areas, such as the Jacobian conjecture, the Linearization problem and the Cancellation problem, can be reformulated in terms of locally nilpotent derivations. This thesis is about the algorithmic study of problems linked to locally nilpotent derivations and their applications to the study of polynomial automorphisms of the affine space. Its aim is to present, on one hand, some problems in which locally nilpotent derivations play a crucial role, namely, the coordinate problem and the parametrization problem. On the other hand, give some algorithms concerning locally nilpotent derivations, which may contribute in understanding locally nilpotent derivations in three dimensional case, namely, rang and triangulability algorithms of locally nilpotent derivations. Créé par EL HOUARI Hassan 29 sept. 2014 Version 0.1

Nature

Thèse de doctorat

Subjects

Disciplines Doctorat/Mathématiques et Applications

Rights

Source

Coverage

Created at

29 sept. 2014

Last modified at

29 sept. 2014

Format

PDF

Language

Author

EL HOUARI Hassan

Last Contributor

system

Contributors

system