Bifurcations in One Dimension. I. The Nonwandering Set.
Bifurcations in One Dimension. II. A Versal Model for Bifurcations.
Bilinear systems and chaos
Billards en polygones et groupes fuchsiens
Billards rationnels et espaces de Teichmüller
Billiard and diophantine approximation
Billiard complexity in the hypercube
We consider the billiard map in the hypercube of . We obtain a language by coding the billiard map by the faces of the hypercube. We investigate the complexity function of this language. We prove that is the order of magnitude of the complexity.
Billiards and boundary traces of eigenfunctions
This is a report on recent results with A. Hassell on quantum ergodicity of boundary traces of eigenfunctions on domains with ergodic billiards, and of work in progress with Hassell and Sogge on norms of boundary traces. Related work by Burq, Grieser and Smith-Sogge is also discussed.
Billiards: models with chaotic dynamics.
Birth of an elliptic island in a chaotic sea.
Blowout bifurcation of chaotic saddles.
Borel summation and splitting of separatrices for the Hénon map
We study two complex invariant manifolds associated with the parabolic fixed point of the area-preserving Hénon map. A single formal power series corresponds to both of them. The Borel transform of the formal series defines an analytic germ. We explore the Riemann surface and singularities of its analytic continuation. In particular we give a complete description of the “first” singularity and prove that a constant, which describes the splitting of the invariant manifolds, does not vanish. An interpretation...
Bound states in completely integrable systems with two types of particles
Braiding of the attractor and the failure of iterative algorithms.
Breaking Cycles on Surfaces.
Brownian motion on a surface of negative curvature
weakly chaotic functions with zero topological entropy and non- flat critical points.
-conjugacy of holomorphic flows near a singularity
C¹-maps having hyperbolic periodic points
We show that the C¹-interior of the set of maps satisfying the following conditions: (i) periodic points are hyperbolic, (ii) singular points belonging to the nonwandering set are sinks, coincides with the set of Axiom A maps having the no cycle property.
C¹-Stably Positively Expansive Maps
The notion of C¹-stably positively expansive differentiable maps on closed manifolds is introduced, and it is proved that a differentiable map f is C¹-stably positively expansive if and only if f is expanding. Furthermore, for such maps, the ε-time dependent stability is shown. As a result, every expanding map is ε-time dependent stable.