Abstract
Our purpose now is to show that the variational tools developed in the two previous chapters (the Aubry set and the action potentials between points) can be used to describe all solutions of the Lax-Oleinik fixed point problem, that is, all calibrated sub-actions. The side effects of the analysis leading to such a result are the beginning of a deeper understanding of the nature of the sub-actions themselves.
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Garibaldi, E. (2017). Representation of Calibrated Sub-actions. In: Ergodic Optimization in the Expanding Case. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-66643-3_6
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DOI: https://doi.org/10.1007/978-3-319-66643-3_6
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