Microlocal Normal Forms for the Magnetic Laplacian

Microlocal normal forms for regular fully nonlinear two-dimensional control systems

In the present paper we deal with fully nonlinear two-dimensional smooth control systems with scalar input q̇ = f(q, u), q ∈ M , u ∈ U , where M and U are differentiable smooth manifolds of respective dimensions two and one. For such systems, we provide two microlocal normal forms, i.e., local in the state-input space, using the fundamental necessary condition of optimality for optimal control p...

Orbital Normal Forms for a family of-zero Singularity

Consider a Dynamical system x'=F(x,µ) such that its linear part has a pair of imaginary eigenvalues and one zero eigenvalue (Hopf zero singularity). Recently, the simplest normal form for this singular system has been obtained by sl(2) Lie algebra theory and the decomposition of space into three invariant subspaces. The normal form of this singular system is divided into three general cases. In...

Cascade Normal Forms for

In this paper, we introduce cascade normal forms for underactuated mechanical systems that are convenient for control design. These normal forms are partially linear which results from a well-known fact that un-deractuated systems can be partially linearized using a change of control 12]. The diiculty arises when the new control appears both in the linear and nonlin-ear subsystems. We introduce...

Normal Forms for the Algebraic Lambda-Calculus

We study the problem of defining normal forms of terms for the algebraic λ-calculus, an extension of the pure λ-calculus where linear combinations of terms are first-class entities: the set of terms is enriched with a structure of vector space, or module, over a fixed semiring. Towards a solution to the problem, we propose a variant of the original reduction notion of terms which avoids annoyin...

Growth and forms of Laplacian aggregates.