Displaying similar documents to “On energy conservation of the simplified Takahashi-Imada method”

Singular Hamiltonian systems and symplectic capacities

Alfred Künzle (1996)

Banach Center Publications

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The purpose of this paper is to develop the basics of a theory of Hamiltonian systems with non-differentiable Hamilton functions which have become important in symplectic topology. A characteristic differential inclusion is introduced and its equivalence to Hamiltonian inclusions for certain convex Hamiltonians is established. We give two counterexamples showing that basic properties of smooth systems are violated for non-smooth quasiconvex submersions, e.g. even the energy conservation...