Jacobi vector fields of integrable geodesic flows

zbMATH Open0937.37010arXivdg-ga/9712017MaRDI QIDQ4951415

Vladimir S. Matveev, Peter Topalov

Publication date: 4 May 2000

Abstract: We show that an invariant surface allows to construct the Jacobi vector field along a geodesic and construct the formula for the normal component of the Jacobi field. If a geodesic is the transversal intersection of two invariant surfaces (such situation we have, for example, if the geodesic is hyperbolic), then we can construct a fundamental solution of the the Jacobi-Hill equation. This is done for quadratically integrable geodesic flows.

Full work available at URL: https://arxiv.org/abs/dg-ga/9712017

zbMATH Keywords

fundamental solutiongeodesic flowfirst integralJacobi equationhyperbolic closed geodesic

Mathematics Subject Classification ID

Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Flows on surfaces (37E35)

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