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VIDEO LIBRARY |
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Focal stability Ch. C. Pugh |
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Abstract: Generically, how many geodesic loops of the same length originate at a common point? Ivan Kupka, Mauricio Peixoto, and I answer this and related questions. We give a fairly sharp bound. Abraham's Bumpy Metric Theorem and its proof by Anosov play a role, as does our focal stability conjecture. This last is a kind of structural stability conjecture for the focal decomposition of the generic exponential map. Namely, we consider a tangent space to a Riemann manifold and divide it into the subsets of vectors having exactly References [1] I. Kupka, M. Peixoto, and C. Pugh, “Focal Stability of Riemann metrics”, J. reine angew. Math., 593, 31–72, (2006). Language: English |