Generic one-parameter families of vector fields on two-dimensional manifolds
Generic properties of the rotation number of one-parameter diffeomorphisms of the circle
Generic robustness of spectral decompositions
Généricité d'exposants de Lyapunov non-nuls pour des produits déterministes de matrices
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...
Geometrical and topological structure of magnetic fields generated by rectilinear wires.
Geometrically finite groups, Patterson-Sullivan measures and Ratner's rigidity theorem.
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 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.
Gibbs states for non-irreducible countable Markov shifts
We study Markov shifts over countable (finite or countably infinite) alphabets, i.e. shifts generated by incidence matrices. In particular, we derive necessary and sufficient conditions for the existence of a Gibbs state for a certain class of infinite Markov shifts. We further establish a characterization of the existence, uniqueness and ergodicity of invariant Gibbs states for this class of shifts. Our results generalize the well-known results for finitely irreducible Markov shifts.
Gibbs-Markov-Young structures*, **, ***
We discuss the geometric structures defined by Young in [9, 10], which are used to prove the existence of an ergodic absolutely continuous invariant probability measure and to study the decay of correlations in expanding or hyperbolic systems on large parts.
Global attractor and finite dimensionally for a class of dissipative equations of BBM's type.
Global attractor of a differentiable autonomous system on the plane
We study the structure of a differentiable autonomous system on the plane with non-positive divergence outside a bounded set. It is shown that under certain conditions such a system has a global attractor. The main result here can be seen as an improvement of the results of Olech and Meisters in [7,9] concerning the global asymptotic stability conjecture of Markus and Yamabe and the Jacobian Conjecture.
Global stability of dynamic systems of high order.
Global theory of ordinary linear homogeneous differential equations in the real domain - II.
Group Actions on Strongly Monotone Dynamical Systems.
Group analysis methods for construction and investigation of the bifurcation equation
Group cohomology and the singularities of the Selberg zeta function associated to a Kleinian group.
Groupoïde d'homotopie d'un feuilletage Riemannien et réalisation symplectique de certaines variétés de Poisson.
The purpose of this paper is to prove the existence of a symplectic realization for a large class of regular Poisson manifolds with Riemannian two dimensional characteristic foliation. To do so, we will show that the homotopy groupoid of a Riemannian foliation is locally trivial.