Now showing items 1-20 of 73

• #### Action-angle variables and a KAM theorem for b-Poisson manifolds ﻿

(2015-02)
External research report
Open Access
In this article we prove an action-angle theorem for b-integrable systems on b-Poisson manifolds improving the action-angle theorem contained in [LMV11] for general Poisson manifolds in this setting. As an application, we ...
• #### Action-angle variables and a KAM theorem for b-Poisson manifolds ﻿

(2016-01-01)
Article
Open Access
In this article we prove an action-angle theorem for b-integrable systems on b-Poisson manifolds improving the action-angle theorem contained in  for general Poisson manifolds in this setting. As an application, we ...
• #### An invitation to singular symplectic geometry ﻿

(2017)
External research report
Open Access
In this paper we analyze in detail a collection of motivating examples to consider bm- symplectic forms and folded-type symplectic structures. In particular, we provide models in Celestial Mechanics for every bm-symplectic ...
• #### An invitation to singular symplectic geometry ﻿

(2019)
Article
Open Access
In this paper we analyze in detail a collection of motivating examples to consider bm-symplectic forms and folded-type symplectic structures. In particular, we provide models in Celestial Mechanics for every bm-symplectic ...
• #### A normal form theorem for integrable systems on contact manifolds ﻿

(2005)
Article
Open Access
We present a normal form theorem for singular integrable systems on contact manifolds
• #### A note on symplectic and Poisson linearization of semisimple Lie algebra actions ﻿

(2015-03)
External research report
Open Access
In this note we prove that an analytic symplectic action of a semisimple Lie algebra can be locally linearized in Darboux coordinates. This result yields simultaneous analytic linearization for Hamiltonian vector fields ...
• #### A note on the symplectic topology of b-manifolds ﻿

(2017)
Article
Open Access
Poisson manifold (M2n; ) is b-symplectic if Vn is transverse to the zero section. In this paper we apply techniques native to Symplectic Topology to address questions pertaining to b-symplectic manifolds. We pro- vide ...
• #### A Poincaré lemma in geometric quantisation ﻿

(American Institute of Mathematical Sciences, 2013-12)
Article
Open Access
This article presents a Poincar e lemma for the Kostant complex, used to compute geometric quantisation, when the polarisation is given by a Lagrangian foliation de ned by an integrable system with nondegenerate singularities.
• #### Classification of b^m-Nambu structures of top degree ﻿

(2018-01)
Article
Open Access
We obtain sufficient conditions for the existence and uniqueness of a positive compact almost automorphic solution to a logistic equation with discrete and continuous delay. Moreover, we provide a counterexample to some ...
• #### Codimension one symplectic foliations and regular Poisson manifolds ﻿

(2010)
External research report
Open Access
In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds, those equipped with a closed one-form defining the symplectic foliation and a closed two-form extending ...
• #### Contact structures with singularities ﻿

(2018-06-15)
External research report
Open Access
We study singular contact structures, which are tangent to a given smooth hypersurface Z and satisfy certain transversality conditions. These singular contact structures are determined by the kernel of non-smooth differential ...
• #### Convexity for Hamiltonian torus actions on b-symplectic manifolds ﻿

(2014-12)
External research report
Open Access
In [GMPS] we proved that the moment map image of a b-symplectic toric manifold is a convex b-polytope. In this paper we obtain convexity results for the more general case of non-toric hamiltonian torus actions on b-symplectic ...
• #### Convexity for Hamiltonian torus actions on b-symplectic manifolds ﻿

(2017)
Article
Open Access
n [GMPS] we proved that the moment map image of a b-symplectic toric manifold is a convex b-polytope. In this paper we obtain convexity results for the more general case of non-toric hamiltonian torus actions on b-symplectic ...
• #### Convexity of the moment map image for torus actions on b(m)-symplectic manifolds ﻿

(Royal Society, 2018-10-28)
Article
Open Access
We prove a convexity theorem for the image of the moment map of a Hamiltonian torus action on a bm-symplectic manifold. This article is part of the theme issue ‘Finite dimensional integrable systems: new trends and methods
• #### Cotangent models for integrable systems on \$b\$-symplectic manifolds ﻿

(2016-01)
External research report
Open Access
• #### Cotangent models of integrable systems ﻿

(2016-07)
Article
Open Access
We associate cotangent models to a neighbourhood of a Liouville torus in symplectic and Poisson manifolds focusing on b-Poisson/b-symplectic manifolds. The semilocal equivalence with such models uses the corresponding ...
• #### Coupling symmetries with Poisson structures ﻿

(2012-10-30)
External research report
Restricted access - author's decision
In this paper we study normal forms problems for integrable systems on Poisson manifolds in the presence of additional symmetries. The symmetries that we consider are encoded in actions of compact Lie groups. The ...
• #### Coupling symmetries with Poisson structures ﻿

(Springer, 2013)
Article
Restricted access - publisher's policy
We study local normal forms for completely integrable systems on Poisson manifolds in the presence of additional symmetries. The symmetries that we consider are encoded in actions of compact Lie groups. The existence of ...
• #### Desingularizing b^m-symplectic structures ﻿

(2017)
Article
Open Access
A 2n-dimensional Poisson manifold (M,Π) is said to be bm-symplectic if it is symplectic on the complement of a hypersurface Z and has a simple Darboux canonical form at points of Z which we will describe below. In this ...
• #### Desingularizing b^m-symplectic structures ﻿

(2015-12)
External research report
Open Access
A 2n-dimensional Poisson manifold (M,¿) is said to be bm-symplectic if it is symplectic on the complement of a hypersurface Z and has a simple Darboux canonical form at points of Z which we will describe below. In this ...
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