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Variational construction of connecting orbits. (English) Zbl 0803.58019

In the context of certain periodic Lagrangian systems, we find sufficient conditions for the existence of an orbit connecting two action minimizing sets. We also find sufficient conditions for the existence of an orbit which visits (to within \(\varepsilon\)) each of a sequence of action minimizing sets, in turn. These results generalize to \(n\) degrees of freedom results previously obtained in 1 degree of freedom (area preserving mappings) [the author, J. Am. Math. Soc. 4, No. 2, 207-263 (1991; Zbl 0737.58029)].

MSC:

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems

Citations:

Zbl 0737.58029
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References:

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