Local $\mathbf {L}^{1}$ estimates for elliptic systems of complex vector fields

construction of vector fields with positive lyapunov exponents

in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...

A dual algorithm for L1-regularized reconstruction of vector fields

Recent advances in vector-field imaging have brought to the forefront the need for efficient denoising and reconstruction algorithms that take the physical properties of vector fields into account and can be applied to large volumes of data. With these requirements in mind, we propose a computationally efficient algorithm for variational denoising and reconstruction of vector fields. Our variat...

Spaces of Local Vector Fields

Vector fields defined only over a part of a manifold give rise to indexes and to transfers. These local vector fields form a topological space whose relation to configuration spaces was studied by Dusa McDuff, and whose higher dimensional homotopy and homology promise invariants of parametrized families of local vector fields. We show that the assignment of the transfer to the vector field give...

Estimates for Elliptic Systems from Composite Material

Carleman estimates for some elliptic systems