E. Garibaldi

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math.DS2026

A Modular Structure Theorem for Minimal Periodic Decompositions and Periodicity of Configurations with $P_{I^} \cdot (4, n) \leq 4 n$

C. F. Colle, E. Garibaldi

Nivat's conjecture asserts that every two-dimensional configuration $I^\cdot : Z^{2} \to A$ whose rectangular pattern complexity satisfies $P_{I^} \cdot (k, n) \leq k n$ for some $…

math.DS2026

Dense periodic optimization for countable Markov shift via Aubry points

Eduardo Garibaldi, JoÃ£o T A Gomes

For transitive Markov subshifts over countable alphabets, this note ensures that a dense subclass of locally HÃ¶lder continuous potentials admits at most a single periodic probabil…

math.DS2025

Maximizing measures for countable alphabet shifts via blur shift spaces

Eduardo Garibaldi, JoÃ£o T A Gomes, Marcelo Sobottka

For upper semi-continuous potentials defined on shifts over countable alphabets, this paper ensures sufficient conditions for the existence of a maximizing measure. We resort to th…

A Modular Structure Theorem for Minimal Periodic Decompositions and Periodicity of Configurations with PI^​⋅(4,n)≤4n

Dense periodic optimization for countable Markov shift via Aubry points

Maximizing measures for countable alphabet shifts via blur shift spaces

A Modular Structure Theorem for Minimal Periodic Decompositions and Periodicity of Configurations with $P_{I^} \cdot (4, n) \leq 4 n$