0000000000274246

AUTHOR

C. A. Morales

showing 3 related works from this author

Singular hyperbolic systems

1999

We construct a class of vector fields on 3-manifolds containing the hyperbolic ones and the geometric Lorenz attractor. Conversely, we shall prove that nonhyperbolic systems in this class resemble the Lorenz attractor: they have Lorenz-like singularities accumulated by periodic orbits and they cannot be approximated by flows with nonhyperbolic critical elements.

Nonlinear Sciences::Chaotic DynamicsMathematics::Dynamical SystemsApplied MathematicsGeneral MathematicsMathematical analysisPhysics::Data Analysis; Statistics and ProbabilityHyperbolic systemsMathematicsProceedings of the American Mathematical Society
researchProduct

Global attractors from the explosion of singular cycles

1997

Abstract In this paper we announce recent results on the existence and bifurcations of hyperbolic systems leading to non-hyperbolic global attractors.

Nonlinear Sciences::Chaotic DynamicsMathematics::Dynamical SystemsMathematical analysisAttractorApplied mathematicsGeneral MedicineDynamical systemMathematics::Geometric TopologyBifurcationHyperbolic systemsMathematicsComptes Rendus de l'Académie des Sciences - Series I - Mathematics
researchProduct

On C1 robust singular transitive sets for three-dimensional flows

1998

Abstract The main goal of this paper is to study robust invariant transitive sets containing singularities for C 1 flows on three-dimensional compact boundaryless manifolds: they are partially hyperbolic with volume expanding central direction. Moreover, they are either attractors or repellers. Robust here means that this property cannot be destroyed by small C 1 -perturbations of the flow.

Transitive relationMathematics::Dynamical SystemsFlow (mathematics)Property (programming)Mathematical analysisAttractorGravitational singularityGeneral MedicineInvariant (mathematics)MathematicsComptes Rendus de l'Académie des Sciences - Series I - Mathematics
researchProduct