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This publication is the 1st to give an summary of higher-order Hamilton geometry with purposes to higher-order Hamiltonian mechanics. it's a direct continuation of the ebook The Geometry of Hamilton and Lagrange areas, (Kluwer educational Publishers, 2001). It comprises the final thought 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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