Integrability, normal forms, and magnetic axis coordinates

Symmetry and integrability in Hamiltonian normal forms

Hölder Forms and Integrability of Invariant Distributions

Abstract. We prove an inequality for Hölder continuous differential forms on compact manifolds in which the integral of the form over the boundary of a sufficiently small, smoothly immersed disk is bounded by a certain multiplicative convex combination of the volume of the disk and the area of its boundary. This inequality has natural applications in dynamical systems, where Hölder forms are ub...

Normal Forms and

In this paper we present a framework for the combination of modal and temporal logic. This framework allows us to combine diier-ent normal forms, in particular, a separated normal form for temporal logic and a rst-order clausal form for modal logics. The calculus of the framework consists of temporal resolution rules and standard rst-order resolution rules. We show that the calculus provides a ...

Fedosov supermanifolds: II. Normal coordinates

The formulation of fundamental physical theories, classical as well as quantum ones, by differential geometric methods nowadays is well established and has a great conceptual virtue. Probably, the most prominent example is the formulation of general relativity on Riemannian manifolds, i.e., the geometrization of the gravitational force; no less important is the geometric formulation of gauge fi...

Poincaré normal and renormalized forms

Normal forms were introduced by Poincaré as a tool to integrate nonlinear systems; by now we know this is in general impossible, but it turned out that the usefulness of normal forms goes well beyond integrability. An introduction to normal forms is provided e.g. in [3, 5, 26, 41, 43, 47, 63]; see also [10, 33]. An introduction to normal forms for Hamiltonian systems is given in appendix 7 of [...