Schrödinger semigroups for vector fields

Schrödinger Semigroups

Let H = \L + V be a general Schrödinger operator on R" (v~> 1), where A is the Laplace differential operator and V is a potential function on which we assume minimal hypotheses of growth and regularity, and in particular allow V which are unbounded below. We give a general survey of the properties of e~, t > 0, and related mappings given in terms of solutions of initial value problems for the d...

Lie algebras Representations and Analytic Semigroups through Dual Vector Fields

Semigroups over Local fields

Let G be a 1-connected, almost-simple Lie group over a local field and S a subsemigroup of G with non-empty interior. The action of the regular hyperbolic elements in the interior of S on the flag manifold G/P and on the associated Euclidean building allows us to prove that the invariant control set exists and is unique. We also provide a characterization of the set of transitivity of the contr...

Control Theory for Semigroups over Local Fields

Let G be a 1-connected, almost-simple Lie group over a local field and S a subsemigroup of G with non-empty interior. The action of the regular hyperbolic elements in the interior of S on the flag manifold G/P and on the associated Euclidean building allows us to prove that the invariant control set exists and is unique. We also provide a characterization of the set of transitivity of the contr...

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...