Geodesic
Entry and leaving arcs of turnpikes: their exact computation in the calculus of variations
Canadian mathematical bulletin, Tome 67 (2024) no. 1, pp. 227-243

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DOI

We settle the question of how to compute the entry and leaving arcs for turnpikes in autonomous variational problems, in the one-dimensional case using the phase space of the vector field associated with the Euler equation, and the initial/final and/or the transversality condition. The results hinge on the realization that extremals are the contours of a well-known function and that the transversality condition is (generically) a curve. An approximation algorithm is presented, and an example is included for completeness.
DOI : 10.4153/S000843952300070X
Mots-clés : Turnpike, saddle, entry and leaving arcs 
Bayón, Luis; Ayuso, Pedro Fortuny; Grau, José María; Ruiz, Maria del Mar. Entry and leaving arcs of turnpikes: their exact computation in the calculus of variations. Canadian mathematical bulletin, Tome 67 (2024) no. 1, pp. 227-243. doi: 10.4153/S000843952300070X
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     title = {Entry and leaving arcs of turnpikes: their exact computation in the calculus of variations},
     journal = {Canadian mathematical bulletin},
     pages = {227--243},
     year = {2024},
     volume = {67},
     number = {1},
     doi = {10.4153/S000843952300070X},
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