Convex model normalized field inverse pushforward
ProvedBirkhoffGlobalSection.convex_model_normalized_field_inverse_pushforwardconvex-geometryreal-analysis
Radial normalization pushes the convex model normalized Hamiltonian field back to its sphere Reeb field.
All displayed regularity, tangency, normalization and supplied-data hypotheses of the exact formal statement are retained. This is a conditional result for the defined convex regularization model, not a global-section or index-existence theorem.
Preamble
import Theorems.Thm_BirkhoffGlobalSection_reverse_radial_variation_bundle open BirkhoffGlobalSection Set Filter SignType open scoped ContDiff Topology set_option linter.unusedVariables false set_option autoImplicit false set_option maxHeartbeats 800000
Formal statement
theorem BirkhoffGlobalSection.convex_model_normalized_field_inverse_pushforward :
∀ {μ c : ℝ}
(M : ConvexRegularizationModel μ c) (y : Phase) (hy : y ∈ frontier M.body),
fderiv ℝ radialNormalize y
((phaseRadialContact y (hamiltonianVectorField M.modelHamiltonian y))⁻¹ •
hamiltonianVectorField M.modelHamiltonian y) =
convexModelSphereReebField M (radialNormalize y) := by sorrySource
Independent extraction of component 7 of the Proved theorem BirkhoffGlobalSection.reverse_radial_variation_bundle. Original verified source: Solutions/Sol_BirkhoffGlobalSection_reverse_radial_variation_bundle.lean. Exact original component retained.