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The study of differentiable manifolds and differentiable maps. One fundamental problem is that of classifying manifolds up to diffeomorphism. Differential topology is what Poincaré understood as topology or “analysis situs”.
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On the existence of regular orbit cylinders
The two multipliers correspond to the exponential growth rate of perturbations 1). Along the periodic orbit, and 2). Normal to energy hypersurface.
Unless there is additional symmetry in the system, t …