Geometric realizations of substitutions
Geometric representations of interacting maps.
Geometric rigidity of invariant measures
Let be a probability measure on which is invariant and ergodic for , and . Let be a local diffeomorphism on some open set. We show that if and , then at -a.e. point . In particular, if is a piecewise-analytic map preserving then there is an open -invariant set containing supp such that is piecewise-linear with slopes which are rational powers of . In a similar vein, for as above, if is another integer and are not powers of a common integer, and if is a -invariant...
Geometric study of a family of integrable systems. (Étude géométrique d'une famille de systémes intégrables.)
Geometrical and topological structure of magnetic fields generated by rectilinear wires.
Geometrical aspects of the Landau-Hall problem on the hiperbolic plane.
Se discuten algunos aspectos del problema de Landau-Hall hiperbólico. El álgebra de Lie de las simetrías infinitesimales de este problema se da explícitamente, resultando ser isomorfa a so(2,1) y que sus invariantes Noether asociados son los momentos angulares hiperbólicos. Asimismo se desarrolla la formulación hamiltoniana, lo que nos permitirá obtener la variedad de órbitas de energía constante de este problema mediante técnicas de reducción simpléctica.
Geometrical methods in hydrodynamics
We describe some recent results on a specific nonlinear hydrodynamical problem where the geometric approach gives insight into a variety of aspects.
Geometrically finite groups, Patterson-Sullivan measures and Ratner's rigidity theorem.
Géométrie algébrique de Poisson et déformations
Géométrie des équations différentielles du second ordre
Géométrie des variétés invariantes d'un difféomorphisme axiome A et transversalité forte
Geometry and dynamics of admissible metrics in measure spaces
We study a wide class of metrics in a Lebesgue space, namely the class of so-called admissible metrics. We consider the cone of admissible metrics, introduce a special norm in it, prove compactness criteria, define the ɛ-entropy of a measure space with an admissible metric, etc. These notions and related results are applied to the theory of transformations with invariant measure; namely, we study the asymptotic properties of orbits in the cone of admissible metrics with respect to a given transformation...
Geometry of currents, intersection theory and dynamics of horizontal-like maps
We introduce a geometry on the cone of positive closed currents of bidegree and apply it to define the intersection of such currents. We also construct and study the Green currents and the equilibrium measure for horizontal-like mappings. The Green currents satisfy some extremality properties. The equilibrium measure is invariant, mixing and has maximal entropy. It is equal to the intersection of the Green currents associated to the horizontal-like map and to its inverse.
Geometry of fluid motion
We survey two problems illustrating geometric-topological and Hamiltonian methods in fluid mechanics: energy relaxation of a magnetic field and conservation laws for ideal fluid motion. More details and results, as well as a guide to the literature on these topics can be found in [3].
Geometry of invariant tori of certain integrable systems with symmetry and an application to a nonholonomic system.
Geometry of Markov systems and codimension one foliations
We show that the theory of graph directed Markov systems can be used to study exceptional minimal sets of some foliated manifolds. A C¹ smooth embedding of a contracting or parabolic Markov system into the holonomy pseudogroup of a codimension one foliation allows us to describe in detail the h-dimensional Hausdorff and packing measures of the intersection of a complete transversal with exceptional minimal sets.
Geometry of non-holonomic diffusion
We study stochastically perturbed non-holonomic systems from a geometric point of view. In this setting, it turns out that the probabilistic properties of the perturbed system are intimately linked to the geometry of the constraint distribution. For -Chaplygin systems, this yields a stochastic criterion for the existence of a smooth preserved measure. As an application of our results we consider the motion planning problem for the noisy two-wheeled robot and the noisy snakeboard.
Geometry of Poisson structures.
Geometry on the group of Hamiltonian diffeomorphisms.
Getting rid of the negative Schwarzian derivative condition.