Related papers: Cotangent bundle reduction and Poincar\'e-Birkhoff…
We develop a functional-analytical machinery for studying the quadratic regulator problem arising from spectra perturbations of infinite-dimensional dynamical systems. In particular, we are interested in applications to inertial manifolds…
In [GT], Goldin and the second author extend some ideas from Schubert calculus to the more general setting of Hamiltonian torus actions on compact symplectic manifolds with isolated fixed points. (See also [Kn99] and [Kn08].) The main goal…
We present a global analysis of the center manifold of the collinear points in the circular restricted three-body problem. The phase-space structure is provided by a family of resonant 2-DOF Hamiltonian normal forms. The near 1:1…
We propose an algebraic scheme for quantizing the rational Ruijsenaars-Schneider model in the R-matrix formalism. We introduce a special parameterization of the cotangent bundle over GL(N,C). In new variables the standard symplectic…
We give a characterization of linear canonoid transformations on symplectic manifolds and we use it to generate biHamiltonian structures for some mechanical systems. Utilizing this characterization we also study the behavior of the harmonic…
For moduli space of stable parabolic bundles on a compact Riemann surface, we derive an explicit formula for the curvature of its canonical line bundle with respect to Quillen's metric and interpret it as a local index theorem for the…
We propose a systematic procedure called the Clebsch canonization for obtaining a canonical Hamiltonian system that is related to a given Lie-Poisson equation via a momentum map. We describe both coordinate and geometric versions of the…
A detailed canonical analysis for Pontryagin and Euler classes with a Barbero-Immirzi [BI] parameter is developed. We rewrite the topological invariants by introducing a set of Holst-like variables, and then study the set of all…
We study the action for the three-space formalism of General Relativity, better known as the BF\'O (Barbour--Foster--\'O Murchadha) action, which is a square-root BSW (Baierlein--Sharp--Wheeler) action. In particular, we explore the…
Several representations of geometric shapes involve quotients of mapping spaces. The projection onto the quotient space defines two sub-bundles of the tangent bundle, called the horizontal and vertical bundle. We investigate in these notes…
Following the Poincare algebra for a free spinning particle and using the Casimirs of the algebra in the Hamiltonian approach, we construct systematically a set of Lagrangians for the relativistic spinning particle which includes the…
On conformally compact manifolds of arbitrary signature, we use conformal geometry to identify a natural (and very general) class of canonical boundary problems. It turns out that these encompass and extend aspects of already known…
Studying high-dimensional Hamiltonian systems with microstructure, it is an important and challenging problem to identify reduced macroscopic models that describe some effective dynamics on large spatial and temporal scales. This paper…
We present new definitions for and give a comprehensive treatment of the canonical compactification of configuration spaces due to Fulton-MacPherson and Axelrod-Singer in the setting of smooth manifolds, as well as a simplicial variant of…
A conformal description of Poincare-Einstein manifolds is developed: these structures are seen to be a special case of a natural weakening of the Einstein condition termed an almost Einstein structure. This is used for two purposes: to shed…
With the covariant formulation in hand from the first paper of this series (physics/9801019), we begin in this second paper to study the canonical (or ``instantaneous'') formulation of classical field theories. The canonical formluation…
We extend the method of controlled Lagrangians with kinetic shaping to those mechanical systems on semidirect product Lie groups with broken symmetry, more specifically to the Euler--Poincar\'e equations with advected parameters. We find a…
This paper develops the notion of implicit Lagrangian systems on Lie algebroids and a Hamilton--Jacobi theory for this type of system. The Lie algebroid framework provides a natural generalization of classical tangent bundle geometry. We…
Minimal varying $\Lambda$ theories are defined by an action built from the Einstein-Cartan-Holst first order action for gravity with the cosmological constant $\Lambda$ as an independent scalar field, and supplemented by the Euler and…
We give a general description of the construction of weighted spherically symmetric metrics on vector bundle manifolds, i.e. the total space of a vector bundle $E\rightarrow M$, over a Riemannian manifold $M$, when $E$ is endowed with a…