On the geometric structure of non-hyperbolic attractors

Abstract

The authors discuss the f( alpha ), spectrum of non-hyperbolic attractors of the Henon type. They elucidate the origin of the 'phase transition' found in a previous paper, and give a lower bound to the spectrum in the non-hyperbolic 'phase' where Kaplan-Yorke-type formulae no longer hold. Their results disagree with other recent attempts. Numerical simulations for the Henon map agree with analytical estimates.