28 citations · 71 across the 27 of their papers we have counts for
22 papers · 1 filter
Flows and Homotopies of Banach Lie algebroids
Fernand Pelletier, Alexander Schmeding
We establish flow and homotopy tools for Banach Lie algebroids that do not rely on compactly supported extensions. Under suitable hypotheses, we construct parameter-dependent local…
Partial Poisson Lie groups and groupoids. Application to Von Neumann algebras
Fernand Pelletier, Patrick Cabau
The purpose of this paper is to propose a version of the notion of convenient Lie groupoid as a generalization of this concept in finite dimension. The authors point out which obst…
Partial Dirac Structures and Dynamical Systems
Fernand Pelletier, Patrick Cabau
In a previous paper (PeCa24), the notion of Dirac structure in finite dimension was extended to the convenient setting. In particular, we introduce the notion of \emph{partial Dira…
Partial Dirac structures in infinite dimension
Fernand Pelletier, Patrick Cabau
In this paper the notion of Dirac structure in finite dimension is extended to the convenient setting. In particular, we introduce the notion of partial Dirac structure on convenie…
Partial Nambu-Poisson structures on a convenient manifold
Patrick Cabau, Fernand Pelletier
This paper offers an adaptation to the convenient setting of finite dimensional Nambu-Poisson structures. In particular, for partial Nambu structures, we look for those whose class…
Structure of finite dimensional linear bundles morphisms
Fernand Pelletier, Patrick Cabau
Let be a fibre bundle over the -dimensional manifold whose typical fibre is the vector space and let be a fibre bundle over the -di…
Smooth Banach structure on orbit spaces and leaf spaces
Daniel Beltita, Fernand Pelletier
We investigate the quotients of Banach manifolds with respect to free actions of pseudogroups of local diffeomorphisms. These quotient spaces are called H-manifolds since the corre…
A survey on partial Nambu-Poisson structures in the convenient setting
Patrick Cabau, Fernand Pelletier
This paper is a survey (may be incomplete) on partial Nambu-Poisson structures in infinite dimension, mainly in the convenient setting. These ones can be seen as a generalization o…
An integrability criterion for a projective limit of Banach distributions
Fernand Pelletier
We give an integrability criterion for a projective limit of Banach distributions on a Fréchet manifold which is a projective limit of Banach manifolds. This leads to a result of i…
Prolongations of convenient Lie algebroids
Patrick Cabau, Fernand Pelletier
We first define the concept of Lie algebroid in the convenient setting. In reference to the finite dimensional context, we adapt the notion of prolongation of a Lie algebroid over…
Projective limit of a sequence of compatible weak symplectic forms on a sequence of Banach bundles and Darboux Theorem
Fernand Pelletier
Given a projective sequence of Banach bundles, each one provided with a of weak symplectic form, we look for conditions under which, the corresponding sequence of weak symplectic f…
Projective and Direct limits of Banach and tensor structures
P. Cabau, F. Pelletier
We endow projective (resp. direct) limits of Banach tensor structures with Fréchet (resp. convenient) structures and study adapted connections to -structures in both frameworks.…
Symmetries of special 2-flags
Piotr Mormul, Fernand Pelletier
This work is a continuation of authors' research interrupted in the year 2010. Derived are recursive relations describing for the first time all infinitesimal symmetries of special…
Convenient Partial Poisson Manifolds
F. Pelletier, P. Cabau
We introduce the concept of partial Poisson structure on a manifold modelled on a convenient space. This is done by specifying a (weak) subbundle of a…
On finsler entropy of smooth distributions and Stefan-Sussman foliations
F. Pelletier
Using the definition of entropy of a family of increasing distances on a compact metric set given in [10] we introduce a notion of Finsler entropy for smooth distributions and Stef…
Möbius transformations and the configuration space of a Hilbert snake
F. Pelletier, R. Saffidine, N Bensalem
The purpose of this paper is to give a simpler proof to the problem of controllability of a Hilbert snake \cite{PeSa}. Using the action of the Möbius group of the unit sphere on th…
Geometrical structures on the prolongation of a pre-Lie algebroid on fibered manifolds and application to Partial Finsler geometry on foliated anchored bundle
F. Pelletier
A pre-Lie algebroid is an anchored bundle provided with an almost Lie bracket such that the anchor is compatible with the Lie bracket of vector fields. We firstly show how most geo…
Integrability on Direct Limit Banach manifolds
Patrick Cabau, Fernand Pelletier
This paper is devoted to the framework of direct limit of anchored Banach bundles over a convenient manifold which is a direct limit of Banach manifold. In particular we give a cri…
Almost Lie structures on an anchored Banach bundle
Patrick Cabau, Fernand Pelletier
Under appropriate assumptions, we generalize the concept of linear almost Poisson struc- tures, almost Lie algebroids, almost differentials in the framework of Banach anchored bund…
Configuration Spaces of a Kinematic System and Monster Tower of Special Multi-Flags
Fernand Pelletier
In this note we show that the configuration spaces of the kinematic system constructed in [4] and [12] gives rise to a natural tower of sphere bundles. Moreover, we prove that, eac…
Integrability of weak distributions on Banach manifolds
Fernand Pelletier
This paper concerns the problem of integrability of non closed distributions on Banach manifolds. We introduce the notion of weak distribution and we look for conditions under whic…
Special 2-flags in lengths not exceeding four: a study in strong nilpotency of distributions
Piotr Mormul, Fernand Pelletier
In the recent years, a number of issues concerning distributions generating 1- flags (called also Goursat flags) has been analyzed. Presently similar questions are discussed as reg…