Abstract: Nonlinear dynamical systems can be uniquely investigated by a geometric theory (KCC-theory). The five KCC-invariants express intrinsic properties of the nonlinear dynamical systems. The second invariant as a curvature tensor determines the stability of the systems. The third invariant as a torsion tensor expresses the chaotic behavior. As an example, the KCC-theory is applied to a geodynamical system (the Rikitake system).
Keywords: Nonlinear dynamical systems, Rikitate system, KCC-theory, Finsler geometry, topological invariant
Classification (MSC2000): 34A26; 34A34, 37N99, 46A63, 53B40, 53B50, 86A25
Full text of the article: