Entire spacelike radial graphs in the Minkowski space, asymptotic to the light-cone, with prescribed scalar curvature
Entropies des flots magnétiques
Entropies et rigidité des espaces localement symétriques de courbure strictement.
Entropy and complexity of a path in sub-riemannian geometry
We characterize the geometry of a path in a sub-riemannian manifold using two metric invariants, the entropy and the complexity. The entropy of a subset of a metric space is the minimum number of balls of a given radius needed to cover . It allows one to compute the Hausdorff dimension in some cases and to bound it from above in general. We define the complexity of a path in a sub-riemannian manifold as the infimum of the lengths of all trajectories contained in an -neighborhood of the path,...
Entropy and complexity of a path in sub-Riemannian geometry
We characterize the geometry of a path in a sub-Riemannian manifold using two metric invariants, the entropy and the complexity. The entropy of a subset A of a metric space is the minimum number of balls of a given radius ε needed to cover A. It allows one to compute the Hausdorff dimension in some cases and to bound it from above in general. We define the complexity of a path in a sub-Riemannian manifold as the infimum of the lengths of all trajectories contained in an ε-neighborhood of the path,...
Entropy of eigenfunctions of the Laplacian in dimension 2
We study asymptotic properties of eigenfunctions of the Laplacian on compact Riemannian surfaces of Anosov type (for instance negatively curved surfaces). More precisely, we give an answer to a question of Anantharaman and Nonnenmacher [4] by proving that the Kolmogorov-Sinai entropy of a semiclassical measure for the geodesic flow is bounded from below by half of the Ruelle upper bound. (This text has been written for the proceedings of the Journées EDP (Port d’Albret-June, 7-11 2010))
Entropy of Geodesic Flow and Exponent of Convergence of Some Dirichlet Series.
Envelopes -- notion and definiteness.
Enveloppe galoisienne d'une application rationnelle de P1.
In 2001, B. Malgrange defines the D-envelope or galoisian envelope of an analytical dynamical system. Roughly speaking, this is the algebraic hull of the dynamical system. In this short article, the D-envelope of a rational map R: P1 --> P1 is computed. The rational maps characterised by a finitness property of their D-envelope appear to be the integrable ones.
Epsilon Nielsen coincidence theory
We construct an epsilon coincidence theory which generalizes, in some aspect, the epsilon fixed point theory proposed by Robert Brown in 2006. Given two maps f, g: X → Y from a well-behaved topological space into a metric space, we define µ ∈(f, g) to be the minimum number of coincidence points of any maps f 1 and g 1 such that f 1 is ∈ 1-homotopic to f, g 1 is ∈ 2-homotopic to g and ∈ 1 + ∈ 2 < ∈. We prove that if Y is a closed Riemannian manifold, then it is possible to attain µ ∈(f, g) moving...
Équation de Hesse pour la détermination des points d'inflexion
Équations de champ symétriques et équations du mouvement sur une variété pseudo-riemannienne à connexion non symétrique
Équations différentielles caractéristiques de la sphère
Equiaffine Darboux motions with double roots
Equiform bundle motions in with spherical trajectories. I.
Equiform bundle motions in with spherical trajectories. II.
Equiform kinematics and the geometry of line elements.
Equipping distributions for linear distribution
In this paper there are discussed the three-component distributions of affine space . Functions , which are introduced in the neighborhood of the second order, determine the normal of the first kind of -distribution in every center of -distribution. There are discussed too normals and quasi-tensor of the second order . In the same way bunches of the projective normals of the first kind of the -distributions were determined in the differential neighborhood of the second and third order.
Equitorsion conform mappings of generalized Riemannian spaces
Equitorsion holomorphically projective mappings of generalized Kählerian space of the first kind
In this paper we define generalized Kählerian spaces of the first kind given by (2.1)–(2.3). For them we consider hollomorphically projective mappings with invariant complex structure. Also, we consider equitorsion geodesic mapping between these two spaces ( and ) and for them we find invariant geometric objects.