Bulletin of the Brazilian Mathematical Society, New Series

Mañé, Ricardo

doi: 10.1007/BF01231694pmid: N/A

We prove a result on the backward dynamics of a rational function nearby a point not contained in the ω-limit set of a recurrent critical point. As a corollary we show that a compact invariant subset of the Julia set, not containing critical or parabolic points, and not intersecting the ω-limit set ofrecurrent critical points, is expanding, thus extending a classical criteria of Fatou. We also prove that the boundary of a Siegel disk is always contained in the ω-limit set of arecurrent critical point.

Viana, Marcelo

doi: 10.1007/BF01231695pmid: N/A

We consider generic one-parameter families of diffeomorphisms on a manifold of arbitrary dimension, unfolding a homoclinic tangency associated to a sectionally dissipative saddle point (the product of any pair of eigenvalues has norm less than 1). We prove that such families exhibit strange attractors in a persistent way: for a positive Lebesgue measure set of parameter values. In the two-dimensional case this had been obtained in a joint work with L. Mora, based on and extending the results of Benedicks-Carleson on the quadratic family in the plane.

Oliveira, M.; Toubiana, Eric

doi: 10.1007/BF01231696pmid: N/A

The existence of nonorientable complete minimal surface of genus two, one end and total curvature −2π(2n+3),n≥3 is proved in this paper.

Brunella, Marco

doi: 10.1007/BF01231697pmid: N/A

We show that any expansive flow on a 3-manifold which is a Seifert fibration or a torus bundle overS 1 is topologically equivalent to a transitive Anosov flow. This is achieved by analyzing the trace of the stable foliation (with singularities) of the flow on incompressible tori embedded in such a manifold.

Stöhr, Karl-Otto

doi: 10.1007/BF01231698pmid: N/A

We describe the pole behaviour of the regular differentials of projective algebraic curves in terms of discrete invariants of the singular points.