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Integrals and variational multipliers of second-order ordinary differential equations

Klapka, Lubomír — 2001

Proceedings of the 20th Winter School "Geometry and Physics"

Summary: Here, a relation between integrals and variational multipliers of a system of second-order ordinary differential equations is studied. A simple necessary and sufficient local condition for the existence of a multiplier is given.

Lagrange functions generating Poisson manifolds of geodesic arcs

Klapka, Lubomír — 2000

Proceedings of the 19th Winter School "Geometry and Physics"

Let $X$ a smooth finite-dimensional manifold and $W_{Γ} (X)$ the manifold of geodesic arcs of a symmetric linear connection $Γ$ on $X$ . In a previous paper [Differential Geometry and Applications (Brno, 1995) 603-610 (1996; Zbl 0859.58011)] the author introduces and studies the Poisson manifolds of geodesic arcs, i.e. manifolds of geodesic arcs equipped with certain Poisson structure. In this paper the author obtains necessary and sufficient conditions for that a given Lagrange function generates a Poisson manifold...

Cauchy atlas on the manifold of all maximal solutions of an ODE system.

Chládek, Petr; Klapka, Lubomír; Udrişte, Constantin — 2005

Balkan Journal of Geometry and its Applications (BJGA)

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Integrals and variational multipliers of second-order ordinary differential equations

Lagrange functions generating Poisson manifolds of geodesic arcs

Cauchy atlas on the manifold of all maximal solutions of an ODE system.