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The ‘time-evolution K-operator’ (or ‘relative Hamiltonian vector field’) in mechanics is a powerful tool which can be geometrically defined as a vector field along the Legendre map. It has been extensively used by several authors for studying the structure and properties of the dynamical systems...
The continuous wavelet transform has become a widely used tool in applied science during the last decade. In this article we discuss some generalizations coming from actions of closed subgroups H of GL(n,R) acting on R
. If R
has finitely many open orbits under the transposed action of H...
A coordinate-free proof of the maximum principle is provided in the specific case of an optimal control problem with fixed time. Our treatment heavily relies on a special notion of variation of curves that consist of a concatenation of integral curves of time-dependent vector fields with unit...
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