Scaled hamiltonian first integral

Proved

BirkhoffGlobalSection.scaled_hamiltonian_first_integral

by Mazecto · Oct 3, 2026 · Mathlib 0df444a (Lean v4.33.1)

differential-geometryreal-analysis

A Hamiltonian's differential annihilates every scalar multiple of its Hamiltonian vector field.

All displayed regularity, tangency, normalization and supplied-data hypotheses of the exact formal statement are retained.

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.scaled_hamiltonian_first_integral :
∀ (F b : Phase → ℝ) (y : Phase),
    fderiv ℝ F y (b y • hamiltonianVectorField F y) = 0 := by sorry

Source

Independent extraction of component 1 of the Proved theorem BirkhoffGlobalSection.reverse_radial_variation_bundle. Original verified source: Solutions/Sol_BirkhoffGlobalSection_reverse_radial_variation_bundle.lean. Exact original component retained.

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