WALKING DROPLETS THROUGH THE LENS OF DYNAMICAL SYSTEMS

The paper is a survey that explicitly states (C1)–(C4) as conjectures and flags them as open problems, e.g., the IDE (4)–(5) and the discrete G2 map (16) are proposed contexts where one might prove pitchforks, period-doubling cascades, and the creation of a global strange attractor as C→1, but no proofs are given in the paper itself. This is stated under “Some conjectures” and revisited again in “Unsolved Problems” . The IDE model structure is introduced (4)–(5) , and the G2 map is defined in (16) , but the claimed phenomena are not proved there. The candidate solution provides plausible outlines for some restricted settings (e.g., with added confinement, small-displacement regimes, and genericity assumptions) and correctly notes that a fully rigorous proof of a robust chaotic strange attractor for the exact IDE is likely open. However, for the G2 map, the candidate asserts a proof of a global strange attractor using a Hénon-like rank-one reduction without verifying the delicate nondegeneracy and parameter-transversality hypotheses; as written, that part remains an incomplete proof sketch rather than a finished proof. Hence, as of the paper’s 2020-11-14 timeframe, the core claims remain likely open.