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The aim of this dissertation is to solve numerically the following problem, denoted by P : given a Riemannian manifold and two points a and b belonging to that manifold, find a tangent vector T at a, such that expa(T) = b, assuming that T exists. This prob ...
This thesis deals with applications of Lie symmetries in differential geometry and dynamical systems. The first chapter of the thesis studies the singular reduction of symmetries of cosphere bundles, the conservation properties of contact systems and their ...
This dissertation investigates wavelets as a multiscale tool on non-Euclidean manifolds. The growing importance of using non-Euclidean manifolds as a geometric model for data comes from the diversity of the data collected. In this work we mostly deal with ...
The effect of sizing on bending rigidity in fibre bundles was investigated. Particular attention was paid to the effect of film formers and anti-static agents on the behaviour of glass fibre bundles under forced packing conditions. The bending rigidity of ...
We consider the L_{q,p}-cohomology of a complete simply connected Riemannian manifold (M,g) with pinched negative curvature. The connection between the L_{q,p}-cohomology of (M,g) and Sobolev inequalities for differential forms on (M,g) was established by ...
This paper describes a two-sweep control design method to stabilize the acrobot, an input-affine under-actuated system, at the upper equilibrium point. In the forward sweep, the system is successively reduced, one dimension at a time, until a two-dimensiona ...
We obtain a theory of stratified Sternberg spaces thereby extending the theory of cotangent bundle reduction for free actions to the singular case where the action on the base manifold consists of only one orbit type. We find that the symplectic reduced sp ...
We investigate the relevance of the metric and of the geometry in five-dimensional models of hadrons. Generically, the metric does not affect strongly the results and even flat space agrees reasonably well with the data. Nevertheless, we observe a preferen ...
Via compression ([18,8]) we write the n-dimensional Chaplygin sphere system as an almost Hamiltonian system on T*SO (n) with internal symmetry group SO (n-1). We show how this symmetry group can be factored out, and pass to the fully reduced system on (a f ...
In this technical report the Discrete Wavelet Frames are build on the already existing Spherical Continuous Wavelet Transform. The spherical half-continuous frames are explored, i.e when the position on the sphere is kept continuous variable. Then, the con ...
