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Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 24, No. 1, pp. 179-189 (2008)
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Nonlinear dynamical systems and KCC-theory

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T. Yajima and Hiroyuki Nagahama

**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

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