Encodings of trajectories and invariant measures

Part A matches Theorem 5: the paper proves shadowing of admissible-path traces via compactness of ε-trajectories and Proposition 2, while the model gives a direct, quantitative argument with a continuous defect functional D on M^Z; both yield the same conclusion (the model omits a harmless constant factor in summing the defect weights). See the paper’s Theorem 5 and its proof strategy via ε-trajectories and Proposition 2 . Part B matches Theorem 9: the paper derives ergodicity of the weak limit of consistent simple-flow traces using the extremal property of simple flows and the h* map from measures to flows, together with (1.4), while the model constructs an inverse-limit symbolic system and a continuous selector Φ to true trajectories, pushing forward an ergodic shift measure and showing μ_k ⇒ μ; the assumptions (successive subdivisions; consistency s_*m_{k+1}=m_k; v(M(i))>0) align with the paper’s setup. See (1.4), Theorem 9, and the surrounding discussion of flows and consistency .