On the emergence and properties of weird quasiperiodic attractors

The paper proves (i) no hyperbolic cycles of period n≥2 can exist and any such cycle must satisfy Pσ(1)=0 (Property 5), (ii) when Pσ(1)=0 and det Jσ≠1, there exist maximal admissible n-cycles of (bounded or one-sided) segments filled with nonhyperbolic σ-cycles (Property 6), and (iii) consequently there are no chaotic attractors under the adopted definition; generically, bounded attractors are either the fixed point O or a WQA. These statements and their proof strategy match the model’s Phase 2 solution almost verbatim, using the same linear homogeneity argument for Fσ and the same segment construction, plus the same chaos definition requiring density of periodic orbits. See Property 5 and 6 and the discussion on chaos and genericity in the paper .