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Chaos theory is the study of systems that are highly sensitive to slight, even imperceptible changes in initial conditions. This is popularly known as the butterfly effect. Many natural systems exhibit chaotic behavior, including weather and electron orbitals.
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Curvature and stability
In Topological methods in hydrodynamics 1 mentioned that "The Riemannian curvature of a manifold has a profound impact on the behavior of geodesics on it. If the Riemannian curvature of a manifold is …