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This booklet is the 1st to provide an outline of higher-order Hamilton geometry with functions to higher-order Hamiltonian mechanics. it's a direct continuation of the e-book The Geometry of Hamilton and Lagrange areas, (Kluwer educational Publishers, 2001). It includes the final idea of upper order Hamilton areas H(k)n, k>=1, semisprays, the canonical nonlinear connection, the N-linear metrical connection and their constitution equations, and the Riemannian nearly touch metrical version of those areas.

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. E C, zero '1 . be the O-dimensional Lie n team generated through the transformation z ~ >. z, z E C - {a}. Then (cf.

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