Abstract
We are now concerned with the existence of sub-actions for Lipschitz continuous potentials. In this chapter, with the aid of a suitable operator, we will show that calibrated sub-actions do exist and can be obtained as solutions of a Lax-Oleinik fixed point problem. Instead making use of a version of the classical Schauder-Tychonoff fixed point theorem, we apply a result due to Ishikawa regarding an iteration process for approximating fixed points of nonexpansive mappings, which, at least in theory, opens up interesting simulation possibilities.
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Garibaldi, E. (2017). 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_3
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DOI: https://doi.org/10.1007/978-3-319-66643-3_3
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