Instability of semi-Riemannian closed geodesics

  title={Instability of semi-Riemannian closed geodesics},
  author={Xijun Hu and Alessandro Portaluri and Ran Yang},
A celebrated result due to Poincare affirms that a closed non-degenerate minimizing geodesic $\gamma$ on an oriented Riemannian surface is hyperbolic. Starting from this classical theorem, our first main result is a general instability criterion for timelike and spacelike closed semi-Riemannian geodesics on a (non)oriented manifold. A key role is played by the spectral index, a new topological invariant that we define through the spectral flow (being the Morse index truly infinite) of a path of… 

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