The algebraic entropy of classical mechanics

الأصل · EN

We describe the `Lie algebra of classical mechanics', modelled on the Lie algebra generated by kinetic and potential energy of a simple mechanical system with respect to the canonical Poisson bracket. It is a polynomially graded Lie algebra, a class we introduce. We describe these Lie algebras, give an algorithm to calculate the dimensions cₙ of the homogeneous subspaces of the Lie algebra of classical mechanics, and determine the value of its entropy ₙ→∞ cₙ¹/ⁿ. It is 1.82542377420108..., a fundamental constant associated to classical mechanics.