Singular strange attractors beyond the boundary of hyperbolic flows
In this paper the authors prove that the suspension of an expanding attractor of a diffeomorphism of the two-disk can be deformed into a robust singular strange attractor which are not Lorenz-like. An attractor is strange if it has a dense orbit with positive Lyapunov exponent and is Lorenz-like if it is singular-hyperbolic and has a unique singularity, it has a basin diffeomorphic to a solid bi-torus and the vector field is inwardly transverse to the boundary of its basin. Although such definition of Lorez-like attractor is not widely used, it fits well they purpose for this work. They perform the deformation along a one-parameter family of flows (an arc of three-dimensional flows) with only one bifurcating parameter value, which allows one to cross the boundary of hyperbolic vector fields, entering in a region completely filled with vector fields that exhibit singular strange attractors.
scientific article; zbMATH DE number 7633388
scientific article