Τοπολογική ταξινόμηση δυναμικών συστημάτων
Περίληψη σε άλλη γλώσσα
The topological classification and study of vector fields is the main theme of this thesis. Chapter 1 contains the definitions and the results on the classification problem on 1 and 2-dimensional manifolds. In Chapter 2, Knot Theory is employed to clarify the topological structure of strange attractors present in 3-d vector fields. In Chapter 3 a procedure is developed which allow (when it can be applied) the global classification of vector fields on R⁴. This procedure is then applied to a number of vector fields of R² and R³. In the final Chapter 4 we study the global structure of a vector field of R³ invariant under the D₂ group. We present its (partial) bifurcation diagram, the dependence of it’s strange attractors on the symmetry and prove the existence of Shilnikov orbits. We conclude with its behavior at infinity.
![]() | |
![]() | Κατεβάστε τη διατριβή σε μορφή PDF (2.86 MB)
(Η υπηρεσία είναι διαθέσιμη μετά από δωρεάν εγγραφή)
|
Όλα τα τεκμήρια στο ΕΑΔΔ προστατεύονται από πνευματικά δικαιώματα.
|