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The 15 pages that link to Poisson bracket, each with the reason it gives.

• Hamiltonian mechanicsRelated: It provides a compact rule for calculating how observables evolve.

• William Rowan HamiltonRelated: Poisson brackets express how dynamical quantities evolve under Hamilton’s equations.

• Lie bracketRelated: It is a Lie bracket on observables, with a direct role in classical mechanics.

• Classical limitRelated: It is the classical counterpart approached by suitably scaled quantum commutators.

• Action-angle variablesRelated: Vanishing Poisson brackets express the compatibility of conserved quantities used to define actions.

• Symplectic geometryRelated: The symplectic form induces a Poisson bracket on smooth functions.

• Jacobi identityRelated: Its Jacobi condition makes the bracket a Lie algebra operation on functions.

• Integrable systemRelated: Vanishing Poisson brackets express the mutual compatibility required of Hamiltonian integrals.

• Symplectic manifoldRelated: The symplectic form induces the Poisson bracket on observables.

• Canonical coordinatesRelated: Its coordinate formula is especially simple for canonical position-momentum pairs.

• Hamiltonian systemRelated: It expresses the time evolution of observables generated by the Hamiltonian.

• Dixmier conjectureRelated: The graded structure carries a Poisson bracket reflecting the Weyl algebra’s commutators.