2009/01/29 by Rodrigo Bissacot, Bissacot, Rodrigo, Eduardo Garibaldi +1 · 1 citation
Computer Science · Mathematics · #Cellular Automata and Applications #Mathematical Dynamics and Fractals #Computability, Logic, AI Algorithms
paper · pdf · doi:10.48550/arxiv.0901.4640
Let \σ: boldsymbol\Σ\→ boldsymbol\Σ be the left shift\nacting on boldsymbol\Σ , a one-sided Markov subshift on a countable\nalphabet. Our intention is to guarantee the existence of \σ-invariant\nBorel probabilities that maximize the integral of a given locally H "older\ncontinuous potential A : boldsymbol\Σ \→ mathbb R . Under certain\nconditions, we are able to show not only that A-maximizing probabilities do\nexist, but also that they are characterized by the fact their support lies\nactually in a particular Markov subshift on a finite alphabet. To that end, we\nmake use of objects dual to maximizing measures, the so-called sub-actions\n(concept analogous to subsolutions of the Hamilton-Jacobi equation), and\nspecially the calibrated sub-actions (notion similar to weak KAM solutions).\n