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The Kuiper Belt is a distant region of the Solar System. On 1 January 2019, the New Horizons spacecraft flew close to (486958) 2014 MU69, a Cold Classical Kuiper Belt Object, a class of objects that have never been heated by the Sun and are therefore well preserved since their formation. Here we describe initial results from these encounter observations. MU69 is a bi-lobed contact binary with a flattened shape, discrete geological units, and noticeable albedo heterogeneity. However, there is little surface color and compositional heterogeneity. No evidence for satellites, ring or dust structures, gas coma, or solar wind interactions was detected. By origin MU69 appears consistent with pebble cloud collapse followed by a low velocity merger of its two lobes., Comment: 43 pages, 8 figure

We endow projective (resp. direct) limits of Banach tensor structures with Fr\'{e}chet (resp. convenient) structures and study adapted connections to $G$-structures in both frameworks. This situation is illustrated by a lot of examples.

We introduce the concept of partial Poisson structure on a manifold $M$ modelled on a convenient space. This is done by specifying a (weak) subbundle $T^{\prime}M$ of $T^{\ast}M$ and an antisymmetric morphism $P:T^{\prime}M\rightarrow TM$ such that the bracket $\{f,g\}_{P}=-$ defines a Poisson bracket on the algebra $\mathcal{A}$ of smooth functions $f$ on $M$ whose differential $df$ induces a section of $T^{\prime}M$. In particular, to each such function $f\in\mathcal{A}$ is associated a hamiltonian vector field $P(df)$. This notion takes naturally place in the framework of infinite dimensional weak symplectic manifolds and Lie algebroids. After having defined this concept, we will illustrate it by a lot of natural examples. We will also consider the particular situations of direct (resp. projective) limits of such Banach structures. Finally, we will also give some results on the existence of (weak) symplectic foliations naturally associated to some particular partial Poisson structures.

Given an ascending sequence of weak symplectic Banach manifolds on which the Darboux theorem is true, we can ask about conditions under which the Darboux Theorem is also true on the direct limit. We will show in general, without very strong conditions, the answer is negative. In particular we give an example of an ascending weak symplectic Banach manifolds on which the Darboux Theorem is true but not on the direct limit. In a second part, we illustrate this discussion in the context of an ascending sequences of Sobolev manifolds of loops in symplectic finite dimensional manifolds. This context gives rise to an example of direct limit of weak symplectic Banach manifolds on which the Darboux theorem is true around any point.

The Pluto system was recently explored by NASA's New Horizons spacecraft, making closest approach on 14 July 2015. Pluto's surface displays diverse landforms, terrain ages, albedos, colors, and composition gradients. Evidence is found for a water-ice crust, geologically young surface units, surface ice convection, wind streaks, volatile transport, and glacial flow. Pluto's atmosphere is highly extended, with trace hydrocarbons, a global haze layer, and a surface pressure near 10 microbars. Pluto's diverse surface geology and long-term activity raise fundamental questions about how small planets remain active many billions of years after formation. Pluto's large moon Charon displays tectonics and evidence for a heterogeneous crustal composition, its north pole displays puzzling dark terrain. Small satellites Hydra and Nix have higher albedos than expected., Comment: 8 pages - Initial Science paper from NASA's New Horizons Pluto Encounter

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 Stefan-Sussmann foliations. This concept generalizes most of classical topological entropy on a compact Riemannian manifold : the entropy of a flow ([9]), of a regular foliation ([11]), of a regular distribution ([5]) and of a geometrical structure ([22]). The essential results of this paper is the nullity of the Finsler entropy for a controllable distribution and for a singular Riemannian foliation.

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 geometrical structures intensively studied in the framework of Lie algebroid can easily be extended in the pre-Lie algebroid context. The principal purpose of this paper is to show that how all these results only depend of the foliated structure and do not depend of the pre-Lie algebroid structure that we can put on a foliated anchored bundle. As application, we obtain a Finsler connection on a foliated anchored bundle which induces the classical Finsler connection on each leaf and a similar result for the Chern connection.

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 M\"obius group of the unit sphere on the configuration space, in the context of a separable Hilbert space. We give a generalization of the Theorem of accessibility contained in \cite{Ha} and \cite{Ro} for articulated arms and snakes in a finite dimensional Hilbert space

In this paper we give a kinematical illustration of some distributions called special multi-flags distributions. Precisely we define the kinematic model in angular coordinates of an articulated arm constituted of a series of (n + 1) segments in Rk+1 and construct the special multi-flag distribution associated to this model.