Related papers: Nonholonomic momentum map reduction and a Chaplygi…

We apply round-off to planar rotations, obtaining a one-parameter family of invertible maps of a two-dimensional lattice. As the angle of rotation approaches pi/2, the fourth iterate of the map produces piecewise-rectilinear motion, which…

In this paper we study coisotropic reduction in multisymplectic geometry. On the one hand, we give an interpretation of Hamiltonian multivector fields as Lagrangian submanifolds and prove that $k$-coisotropic submanifolds induce a Lie…

A method, called beatification, is presented for rapidly extracting weakly nonlinear Hamiltonian systems that describe the dynamics near equilibria for systems possessing Hamiltonian form in terms of noncanonical Poisson brackets. The…

We study the relativistic formulation of a classical time-dependent nonholonomic Lagrangian mechanics from the perspective of moving frames. We also introduce time-dependent $G$-Chaplygin systems with affine constraints, which are natural…

In this work, we consider a specific space of foliations with $C^1$ leaves and H\"older holonomies of the square $M=[0,1]^2$, with some topology and we show that a generic such foliation is non-absolutely continuous, furthermore, the…

This paper presents a Hamiltonian reduction procedure for field theories over affine principal bundles introducing a canonical identification to describe the reduced multisymplectic space without the introduction of a connection. The main…

Let $(X, \omega)$ be a compact symplectic manifold and $L$ be a Lagrangian submanifold. Suppose $(X, L)$ has a Hamiltonian $S^1$ action with moment map $\mu$. Take an invariant $\omega$-compatible almost complex structure, we consider…

We prove the a.e. nonamenability of locally finite quasi-pmp Borel graphs whose every component admits at least three nonvanishing ends with respect to the underlying Radon--Nikodym cocycle. We witness their nonamenability by constructing…

We study Hamiltonian systems near a compact symplectic Morse-Bott minimum. Our first result shows that if the flow is Zoll (that is, it induces a free circle action) along a sequence of energy levels converging to the minimum, then the…

We consider random dynamical systems such as groups of conformal transformations with a probability measure, or transversaly conformal foliations with a Laplace operator along the leaves, in which case we consider the holonomy pseudo-group.…

In this paper we study contact nonholonomic mechanical sys\-tems. We construct a general framework for non-holonomic constraints in contact geometry and, in this framework, we define different nonholonomic brackets using con\-venient…

H-holomorphic maps are a parameter version of J-holomorphic maps into contact manifolds. They have arisen in efforts to prove the existence of higher--genus holomorphic open book decompositions and efforts to prove the existence of finite…

The main result of this paper is a quasi-hamiltonian analogue of a special case of the O'Shea-Sjamaar convexity theorem for usual momentum maps. We denote by U a simply connected compact connected Lie group and we fix an involutive…

Geometric conditions are given so that the leafwise reduced cohomology is of infinite dimension, specially for foliations with dense leaves on closed manifolds. The main new definition involved is the intersection number of subfoliations…

Some aspects of the geometry and the dynamics of generalized Chaplygin systems are investigated. First, two different but complementary approaches to the construction of the reduced dynamics are reviewed: a symplectic approach and an…

The $\text{PSL}(4,\mathbb{R})$ Hitchin component of a closed surface group $\pi_1(S)$ consists of holonomies of properly convex foliated projective structures on the unit tangent bundle of $S$. We prove that the leaves of the…

We construct multisymplectic formulations of fluid dynamics using the inverse of the Lagrangian path map. This inverse map -- the ``back-to-labels'' map -- gives the initial Lagrangian label of the fluid particle that currently occupies…

The purpose of this note is twofold. First we show that, for weakly differentiable maps between Riemannian manifolds of any dimension, a smallness condition on a Morrey-norm of the gradient is sufficient to guarantee that the pulled-back…

We investigate the Poisson geometry of the Marsden-Weinstein reductions of the moment map associated to the cotangent bundle of the space of representations of a quiver. We show that the stratification by representation type equals the…

In this paper we use an affine connection formulation to study an optimal control problem for a class of nonholonomic, under-actuated mechanical systems. In particular, we aim at minimizing the norm-squared of the control input to move the…