C. M. Carballo

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math.DS2003

Omega-limit sets close to singular-hyperbolic attractors

C. M. Carballo, C. A. Morales

We study the omega-limit sets $ω_{X} (x)$ in an isolating block $U$ of a singular-hyperbolic attractor for three-dimensional vector fields $X$ . We prove that for every vector field $Y…

math.DS2001

Homoclinic classes for generic C^1 vector fields

C. M. Carballo, C. A. Morales, M. J. Pacifico

We prove that homoclinic classes for a residual set of C^1 vector fields X on closed n-manifolds are maximal transitive and depend continuously on periodic orbit data. In addition,…

math.DS2001

Homoclinic classes and finitude of attractors for vector fields on n-manifolds

C. M. Carballo, C. A. Morales

A homoclinic class of a vector field is the closure of the transverse homoclinic orbits associated to a hyperbolic periodic orbit. An attractor (a repeller) is a transitive set to…