87 citations · 877 across the 97 of their papers we have counts for
27 papers · 1 filter
The restricted Siegel disc as coadjoint orbit
François Gay-Balmaz, Tudor S. Ratiu, Alice B. Tumpach
The restricted Siegel disc is a homogeneous space related to the connected component of the Universal Teichmüller space via the period mapping. In this paper we show that…
Symplectic Induction, Prequantum Induction, and Prequantum Multiplicities
Tudor S. Ratiu, Francois Ziegler
Frobenius reciprocity asserts that induction from a subgroup and restriction to it are adjoint functors in categories of unitary G-modules. In the 1980s, Guillemin and Sternberg es…
Convexity of singular affine structures and toric-focus integrable Hamiltonian systems
Tudor Ratiu, Christophe Wacheux, Nguyen Tien Zung
This work is devoted to a systematic study of symplectic convexity for integrable Hamiltonian systems with elliptic and focus-focus singularities. A distinctive feature of these sy…
Presymplectic convexity and (ir)rational polytopes
Tudor Ratiu, Nguyen Tien Zung
In this paper, we extend the Atiyah--Guillemin--Sternberg convexity theorem and Delzant's classification of symplectic toric manifolds to presymplectic manifolds. We also define an…
The tropical momentum map: a classification of toric log symplectic manifolds
Marco Gualtieri, Songhao Li, Alvaro Pelayo +1
We give a generalization of toric symplectic geometry to Poisson manifolds which are symplectic away from a collection of hypersurfaces forming a normal crossing configuration. We…
L^2-Cohomology and complete Hamiltonian manifolds
Rafe Mazzeo, Álvaro Pelayo, Tudor Ratiu
A classical theorem of Frankel for compact Kähler manifolds states that a Kähler S^1-action is Hamiltonian if and only if it has fixed points. We prove a metatheorem which says tha…
Poisson Reduction of Controlled Hamiltonian System by Controllability Distribution
Tudor S. Ratiu, Hong Wang
In this paper, we first study the Poisson reductions of controlled Hamiltonian (CH) system and symmetric CH system by controllability distributions. These reductions are the extens…
The affine invariant of generalized semitoric systems
Álvaro Pelayo, Tudor S. Ratiu, San Vũ Ngoc
A generalized semitoric system F:=(J,H): M --> R^2 on a symplectic 4-manifold is an integrable system whose essential properties are that F is a proper map, its set of regular valu…
Moduli spaces of toric manifolds
Álvaro Pelayo, Ana Rita Pires, Tudor S. Ratiu +1
We construct a distance on the moduli space of symplectic toric manifolds of dimension four. Then we study some basic topological properties of this space, in particular, path-conn…
Applying Hodge theory to detect Hamiltonian flows
Alvaro Pelayo, Tudor S. Ratiu
We prove that when Hodge theory survives on non-compact symplectic manifolds, a compact symplectic Lie group action having fixed points is necessarily Hamiltonian, provided the ass…
Extensions of Lie-Rinehart algebras and cotangent bundle reduction
Johannes Huebschmann, Matthew Perlmutter, Tudor S. Ratiu
Let Q denote a smooth manifold acted upon smoothly by a Lie group G. The G-action lifts to an action on the total space T of the cotangent bundle of Q and hence on the standard sym…
The momentum map in Poisson geometry
Rui Loja Fernandes, Juan-Pablo Ortega, Tudor S. Ratiu
Every action on a Poisson manifold by Poisson diffeomorphisms lifts to a Hamiltonian action on its symplectic groupoid which has a canonically defined momentum map. We study variou…
Metric convexity in the symplectic category
Petre Birtea, Juan-Pablo Ortega, Tudor S. Ratiu
We introduce an extension of the standard Local-to-Global Principle used in the proof of the convexity theorems for the momentum map to handle closed maps that take values in a len…
Openness and convexity for momentum maps
Petre Birtea, Juan-Pablo Ortega, Tudor S. Ratiu
The purpose of this paper is finding the essential attributes underlying the convexity theorems for momentum maps. It is shown that they are of topological nature; more specificall…
Cotangent bundle reduction
Juan-Pablo Ortega, Tudor S. Ratiu
This encyclopedia article briefly reviews without proofs some of the main results in cotangent bundle reduction. The article recalls most the necessary prerequisites to understand…
Poisson reduction
Juan-Pablo Ortega, Tudor S. Ratiu
This encyclopedia article briefly reviews without proofs some of the main results in Poisson reduction. The article recalls most the necessary prerequisites to understand the main…
Symmetry and symplectic reduction
Juan-Pablo Ortega, Tudor S. Ratiu
This encyclopedia article briefly reviews without proofs some of the main results in symplectic reduction. The article recalls most the necessary prerequisites to understand the ma…
Singular cosphere bundle reduction
Oana Dragulete, Tudor S. Ratiu, Miguel Rodriguez-Olmos
This paper studies singular contact reduction for cosphere bundles at the zero value of the momentum map. A stratification of the singular quotient, finer than the contact one and…
The reduced spaces of a symplectic Lie group action
Juan-Pablo Ortega, Tudor S. Ratiu
There exist three main approaches to reduction associated to canonical Lie group actions on a symplectic manifold, namely, foliation reduction, introduced by Cartan, Marsden-Weinst…
Symplectic leaves in real Banach Lie-Poisson spaces
Daniel Beltiţă, Tudor S. Ratiu
We present several large classes of real Banach Lie-Poisson spaces whose characteristic distributions are integrable, the integral manifolds being symplectic leaves just as in fini…
Extensions of Banach Lie-Poisson spaces
Anatol Odzijewicz, Tudor Ratiu
The extension of Banach Lie-Poisson spaces is studied and linked to the extension of a special class of Banach Lie algebras. The case of W*-algebras is given particular attention.…
The Banach Poisson geometry of multi-diagonal Toda-like lattices
Anatol Odzijewicz, Tudor Ratiu
The Banach Poisson geometry of multi-diagonal Hamiltonian systems having infinitely many integrals in involution is studied. It is shown that these systems can be considered as gen…
The relation between local and global dual pairs
James Montaldi, Juan-Pablo Ortega, Tudor S. Ratiu
In this note we clarify the relationship between the local and global definitions of dual pairs in Poisson geometry. It turns out that these are not equivalent. For the passage fro…
Banach Lie-Poisson spaces and reduction
Anatol Odzijewicz, Tudor S. Ratiu
The category of Banach Lie-Poisson spaces is introduced and studied. It is shown that the category of W*-algebras can be considered as one of its subcategories. Examples and applic…