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Dynamical Systems, Flows & Geometry

Zeros as fixed points of flows and features of geometric spaces.

What this theme is

Papers here treat the critical line as an attractor or invariant of a dynamical system, study geodesic and transfer-operator flows, exploit fractal strings and self-similar geometry, and frame the rigidity of the zeros geometrically. The Lapidus theory of fractal strings and spectral geometry sits squarely here.

Why it recurs

Dynamics and geometry recur because they give RH a shape: a flow whose stable set is the critical line, or a space whose spectrum is the zeros. They also connect naturally to quantum chaos, where geodesic flow on a chaotic surface has GUE statistics.

Relevance to the Riemann Hypothesis

If the critical line is a stable attractor or a forced geometric symmetry axis, zeros cannot escape it. Fractal-string formulations turn RH into a statement about the optimal error in Weyl's law for spectral counting functions.