Symbolic dynamics for non-uniformly hyperbolic flows in high dimension

The uploaded paper proves (with full details) the existence, for each fixed χ>0, of a single locally compact topological Markov flow (Σ_r,σ_r) with Hölder roof and a Hölder semiconjugacy π_r that simultaneously codes a full-measure set for every χ–hyperbolic invariant measure and is finite-to-one on the regular set; this is their Main Theorem and Theorem 9.1, including parts (1)–(3) and further structure properties . In contrast, the candidate solution asserts a uniform positive lower bound on the roof/transition times (a τ_min>0) and on r, which the paper does not claim and is generally false in this construction: the roof is only required to be positive and uniformly bounded above (r̂: Σ̂→(0,ρ)), and short holonomy returns can make transition times arbitrarily small (see the definition of r̂ and Proposition 9.3, and the discussion around holonomy maps) . The model also glosses over the key, delicate local finiteness step, which in the paper depends on their inverse theorem and the refinement to a locally finite Markov cover Z before producing the final Markov partition; it is not a straightforward consequence of discretization as the model claims (see the method of proof and Section 7 leading into Section 9) . Therefore, while the model’s high-level outline tracks the paper’s scheme, it contains incorrect claims and missing arguments; the paper’s argument is correct and complete for the stated results.