By R. Miron
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 booklet The Geometry of Hamilton
and Lagrange Spaces, (Kluwer educational Publishers, 2001). It comprises the overall concept 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 virtually touch metrical version of those areas. additionally, the quantity additionally describes new advancements resembling variational ideas for
larger order Hamiltonians; Hamilton-Jacobi equations; greater order energies and legislation of conservation; Noether symmetries; Hamilton subspaces of order ok and their basic equations. The duality, through Legendre transformation,
among Hamilton areas of order okay and Lagrange areas of an analogous order is mentioned. additionally, the geometry of Cartan areas of order okay =1 is investigated intimately. This thought comes in handy within the development of geometrical
types in theoretical physics, mechanics, dynamical platforms, optimum keep watch over, biology, economic system and so on.
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