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On different geometric formulations of Lagrangian formalism. (English) Zbl 0930.58001
We consider two geometric formulations of Lagrangian formalism on fibred manifolds: Krupka’s theory of finite order variational sequences, and Vinogradov’s infinite order variational sequence associated with the $$C$$-spectral sequence. On the one hand, we show that the direct limit of Krupka’s variational bicomplex is a new infinite order variational bicomplex which yields a new infinite order variational sequence. On the other hand, by means of Vinogradov’s $$C$$-spectral sequence, we provide a new finite order variational sequence whose direct limit turns out to be Vinogradov’s infinite order variational sequence. Finally, we provide an equivalence of the two finite order and infinite order variational sequences up to the space of Euler-Lagrange morphisms.
Reviewer: R.Vitolo (Lecce)

##### MSC:
 58A12 de Rham theory in global analysis 58A20 Jets in global analysis 58E30 Variational principles in infinite-dimensional spaces 58J10 Differential complexes
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