학술논문
The multidimensional Lorenz attractor is a homoclinic class.
Document Type
Journal
Author
Bautista, S. (CL-UNC-NDM) AMS Author Profile; Rojas, J. D. (BR-IMPA) AMS Author Profile
Source
Subject
37 Dynamical systems and ergodic theory -- 37D Dynamical systems with hyperbolic behavior
37D45Strange attractors, chaotic dynamics
37D45
Language
English
Abstract
The multidimensional Lorenz attractor first appeared in [C. Bonatti,A. Pumariño and M. Viana, C. R. Acad. Sci. Paris Sér. I Math. {\bf 325}(1997), no.~8, 883--888; MR1485910 (98m:58082)]. It is one ofthe first examples of a robusttransitive attractor containing a singularity with any number ofexpanding eigenvalues. The example was constructed in a manifold withdimension greater than three. In this paper, the authors apply theargument in [S. Bautista, Bol. Mat. {\bf 11} (2004), no.~1, 69--78; MR2144882 (2005m:37069)]to show that the geometric Lorenz attractor is a homoclinic classand prove that the multidimensional Lorenz attractors are homoclinicclasses.