Lorenz-like chaotic attractors revised
Dynamical Systems
2010-08-31 v2
Abstract
We describe some recent results on the dynamics of singular-hyperbolic (or Lorenz-like) attractors: attractors in this class are expansive and so sensitive with respect to initial data; they admit a unique physical measure whose support is the whole attractor, which is hyperbolic and the equilibrium state with respect to the center-unstable Jacobian; the hitting time associated to a geometric Lorenz attractor satisfies a logarithm law; the rate of large deviations for the physical measure on the ergodic basin of a geometric Lorenz attractor is exponential.
Keywords
Cite
@article{arxiv.0804.3617,
title = {Lorenz-like chaotic attractors revised},
author = {Vitor Araujo and Maria Jose Pacifico},
journal= {arXiv preprint arXiv:0804.3617},
year = {2010}
}
Comments
19 pages, 6 figures, short survey paper for the Springer Proceedings associated to the DYNA2008 Conference: Dynamics & Applications in honour of Mauricio Peixoto and David Rand