The algebraic entropy of classical mechanics
نویسندگان
چکیده
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 limn→∞ c 1/n n . It is 1.82542377420108 . . ., a fundamental constant associated to classical mechanics. ∗Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand ([email protected]).
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