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Properties of Minimum Action Curves

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Book cover Minimum Action Curves in Degenerate Finsler Metrics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2134))

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Abstract

In this chapter we study the properties of minimum action curves, often focusing on a specific subclass of actions. First we show which points minimizing curves can pass “in infinite length.” Then we find for a certain type of Hamiltonian actions that the action of the drift vector field’s flowlines vanishes, and that bending curves into the direction of the drift reduces their action. As a consequence, we then prove the non-existence of minimizers in some situations, and we show that minimizers leading from one attractor of the drift to another have to pass a saddle point on the separatrix between the two basins of attraction.

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Authors and Affiliations

  1. Mathematics Department, Duke University, Durham, North Carolina, USA

    Matthias Heymann

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  1. Matthias Heymann
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Heymann, M. (2015). Properties of Minimum Action Curves. In: Minimum Action Curves in Degenerate Finsler Metrics. Lecture Notes in Mathematics, vol 2134. Springer, Cham. https://doi.org/10.1007/978-3-319-17753-3_4

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