A solution to the bidimensional global asymptotic stability conjecture
A stability theorem for foliations with singularities [Book]
A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms. I.
A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms. II.
A sufficient condition for -stability of vector fields on open manifolds
A theorem on the structural stability of non-autonomous differential equations
A topological characterization of holomorphic parabolic germs in the plane
J.-M. Gambaudo and É. Pécou introduced the "linking property" in the study of the dynamics of germs of planar homeomorphisms in order to provide a new proof of Naishul's theorem. In this paper we prove that the negation of the Gambaudo-Pécou property characterizes the topological dynamics of holomorphic parabolic germs. As a consequence, a rotation set for germs of surface homeomorphisms around a fixed point can be defined, and it turns out to be non-trivial except for countably many conjugacy classes....
A topological version of a theorem of Mather on shadowing in monotone twist maps
A turnpike theorem for continuous-time control systems when the optimal stationary point is not unique.
A version of non-Hamiltonian Liouville equation
In this paper we give a version of the theorem on local integral invariants of systems of ordinary differential equations. We give, as an immediate conclusion of this theorem, a condition which guarantees existence of an invariant measure of local dynamical systems. Results of this type lead to the Liouville equation and have been frequently proved under various assumptions. Our method of the proof is simpler and more direct.
About Stefan's definition of a foliation with singularities : a reduction of the axioms
Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows
We consider volume-preserving perturbations of the time-one map of the geodesic flow of a compact surface with negative curvature. We show that if the Liouville measure has Lebesgue disintegration along the center foliation then the perturbation is itself the time-one map of a smooth volume-preserving flow, and that otherwise the disintegration is necessarily atomic.
Absolutely extremal points in minimal flows
Abundance of hyperbolicity in the topology
Accessibility of typical points for invariant measures of positive Lyapunov exponents for iterations of holomorphic maps
We prove that if A is the basin of immediate attraction to a periodic attracting or parabolic point for a rational map f on the Riemann sphere, if A is completely invariant (i.e. ), and if μ is an arbitrary f-invariant measure with positive Lyapunov exponents on ∂A, then μ-almost every point q ∈ ∂A is accessible along a curve from A. In fact, we prove the accessibility of every “good” q, i.e. one for which “small neigh bourhoods arrive at large scale” under iteration of f. This generalizes the...
Action minimizing invariant measures for positive definite Lagrangian systems.
Actions localement libres de groupes non unimodulaires
Actions localement libres de groupes résolubles
Soient un groupe de Lie connexe de dimension , une action localement libre de classe de sur une variété compacte de dimension . Nous supposons qu’il existe dans l’algèbre de Lie de un champ tel que les valeurs propres de soient avec . Alors, nous montrons que est -conjuguée à une “action modèle" de sur un espace homogène où est un groupe de Lie contenant . Si , est uniquement déterminé par ; si , il y a deux groupes possibles, et nous pouvons donc donner une...
Affine diffeomorphisms of translation surfaces : periodic points, fuchsian groups, and arithmeticity
Algebraic periods of self-maps of a rational exterior space of rank 2.