Jacobi stability analysis of dynamical systems—applications in gravitation and cosmology

• DOI: 10.4310/atmp.2012.v16.n4.a2
• Publication Date: 2013-08-30T21:01:56Z
• Authors: C. G. Böhmer; T. Harko; S. V. Sabau
• Keywords: 0103 physical sciences; FOS: Mathematics; FOS: Physical sciences; Mathematical Physics (math-ph); General Relativity and Quantum Cosmology (gr-qc); Dynamical Systems (math.DS); Mathematics - Dynamical Systems; 01 natural sciences; Mathematical Physics; General Relativity and Quantum Cosmology

The Kosambi-Cartan-Chern (KCC) theory represents a powerful mathematical method for the analysis of dynamical systems.In this approach, one describes evolution system in geometric terms, by considering it as geodesic Finsler space.By associating non-linear connection and Berwald-type to system, five geometrical invariants are obtained, with second invariant giving Jacobi stability system.The (in)stability is natural generalization flow on differentiable manifold endowed metric (Riemannian or Finslerian)