Ergodic Optimization for Continuous Functions on the Dyck-Motzkin Shifts

The uploaded paper proves exactly the three items in question for Dyck–Motzkin shifts: generic zero-entropy maximizers (Theorem A(a)), a dense set of potentials with uncountably many fully supported Bernoulli maximizers (Theorem A(b)), and path connectedness plus local path connectedness of the ergodic-measure space (Theorem B). The model’s solution explicitly invokes and sketches the same ingredients: density of periodic (CO) measures, abundance of high-complexity paths, and an Israel/Bishop–Phelps tangency scheme, mirroring the paper’s proofs. Minor presentation differences (e.g., the model’s optional “piecewise homeomorphism” remark and a direct separation argument for (A)(a)) do not alter correctness. See Theorem A and its proof outline, including use of CO-measure density and Morris’s result, and the construction of high-complexity paths leading to Theorem B in the paper .