| import OAI.Geometry.Arnold.Degeneracy | |
| namespace OAI | |
| noncomputable section | |
| open scoped BigOperators ContDiff | |
| open scoped Topology NNReal | |
| open Set Filter | |
| namespace ArnoldCounterexample | |
| /-- The Hamiltonian counterexample, with the complete fixed set, the lower bound | |
| for all smooth functions, and a genuine nonzero quotient-tangent eigenvector. -/ | |
| theorem main : | |
| ∃ φ : Q3 ≃ Q3, IsHamiltonian φ ∧ (fixedSet φ).encard = 3 ∧ | |
| (3 : ℕ∞) < 4 ∧ 4 ≤ criticalNumber ∧ HasDegenerateFixedPoint φ := by | |
| exact ⟨Construction.mainEquiv, Construction.main_isHamiltonian, | |
| Construction.main_fixed_encard, by norm_num, four_le_criticalNumber, | |
| Construction.main_degenerate⟩ | |
| end ArnoldCounterexample | |
| end | |
| end OAI | |