Geometry and Chaos
The purpose of the present chapter is to describe in some detail how it is possibile, using the Jacobi–Levi-Civita equation for geodesic spread as the main tool, to reach a twofold objective: first, to obtain a deeper understanding of the origin of chaos in Hamiltonian systems, and second, to obtain quantitative information on the “strength” of chaos in these systems.
KeywordsLyapunov Exponent Sectional Curvature Ricci Curvature Jacobi Equation Stability Equation
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