Lorenz-like chaotic attractors revised

Details Lorenz-like chaotic attractors revised Lorenz-like chaotic attractors revised

2008-04-22

arxiv.org/abs/0804.3617v2

DYNA2008, in Honour of Maur\'icio Peixoto and David Rand, September 8-12, 2008, University of Minho, Braga, Portugal Series: S

Mathematics

Dynamical Systems

19 pages, 6 figures, short survey paper for the Springer Proceedings associated to the DYNA2008 Conference: Dynamics & Applica

Scientific paper

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.

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