Multidimensional Rovella-like attractors

作者：Araujo V^*; Castro A; Pacifico M J; Pinheiro V

来源：Journal of Differential Equations, 2011, 251(11): 3163-3201.

DOI：10.1016/j.jde.2011.07.021

• Singular flow
• Physical measure
• Dominated decomposition
• Multidimensional non-uniform expansion

We present a multidimensional flow exhibiting a Rovella-like attractor: a transitive invariant set with a non-Lorenz-like singularity accumulated by regular orbits and a multidimensional non-uniformly expanding invariant direction. Moreover, this attractor has a physical measure with full support and persists along certain sub-manifolds of the space of vector fields. As in the 3-dimensional Rovella-like attractor, this example is not robust. As a sub-product of the construction we obtain a new class of multidimensional non-uniformly expanding endomorphisms without any uniformly expanding direction, which is interesting by itself. Our example is a suspension (with singularities) of this multidimensional endomorphism.

• 出版日期2011-12-1