The authors introduce an electromagnetic curvature criterion for linear stability of relative equilibria in the planar n-body problem, recovering Routh's criterion for three bodies and providing an instability test when dynamics split into symplectic planes.
Lectures on the free period Lagrangian action functional.J
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An abstract perturbation theorem turns compact zero sets of Fredholm sections into nearby compact smooth manifolds (preserving transverse loci), enabling cobordisms and a re-proof of Schwarz's action spectrum result.
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Relative equilibria, linear stability and electromagnetic curvature
The authors introduce an electromagnetic curvature criterion for linear stability of relative equilibria in the planar n-body problem, recovering Routh's criterion for three bodies and providing an instability test when dynamics split into symplectic planes.
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An Abstract Perturbation Theorem for Compact Moduli Spaces
An abstract perturbation theorem turns compact zero sets of Fredholm sections into nearby compact smooth manifolds (preserving transverse loci), enabling cobordisms and a re-proof of Schwarz's action spectrum result.