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720fa25 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | 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
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