Strong unique continuation for 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...

Unique Continuation Principle for Systems of Parabolic Equations

In this paper we prove a unique continuation result for a cascade system of parabolic equations, in which the solution of the first equation is (partially) used as a forcing term for the second equation. As a consequence we prove the existence of ε-insensitizing controls for some parabolic equations when the control region and the observability region do not intersect. Mathematics Subject Class...

Integration of Complex Vector Fields

(1.3) Lku = 0, k = 1,. . . , m. Any function u satisfying all the above equations must also satisfy the equations (1.4) [Lk9 Lh]u = LkLhu LhLku = 0. Thus it is reasonable to assume that the space spanned by the vector fields Lu..., Lm is closed under the bracket operation. Condition A. This condition is satisfied if (1.5) [Lk,IJ = I 4 ^ j where the a^6C°°((7). From (1.2) we obtain [Lk,Lh]u = Lk...

Unique Normal Forms for Nilpotent Planar Vector Fields

Strong Unique Continuation for Products of Elliptic Operators of Second Order

We study strong unique continuation for products of elliptic operators. The main tools are Carleman inequalities for second order elliptic operators. We obtain strong unique continuation assuming either Gevrey regularity of the coefficients or some pointwise conditions on the coefficients.