Journal of Mathematics of Kyoto University
- J. Math. Kyoto Univ.
- Volume 46, Number 2 (2006), 303-348.
On the basin problem for Hénon-like attractors
The basin problem for a strange attractor asks the asymptotic distribution of Lebesgue almost every initial point in the basin of attraction. A solution to this problem for Hénon-like attractors was initially given by Benedicks-Viana, and later by Wang-Young, under certain assumptions on the Jacobian of the map, which are used in a crucial way to control the growth of volumes under iteration. The purpose of this paper is to remove the assumption on the Jacobian in their solutions, in a hope that the argument can be extended to a broader class of Hénon-like maps which are not necessarily invertible and possess singularities.
J. Math. Kyoto Univ., Volume 46, Number 2 (2006), 303-348.
First available in Project Euclid: 14 August 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 37D45: Strange attractors, chaotic dynamics
Secondary: 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces
Takahasi, Hiroki. On the basin problem for Hénon-like attractors. J. Math. Kyoto Univ. 46 (2006), no. 2, 303--348. doi:10.1215/kjm/1250281779. https://projecteuclid.org/euclid.kjm/1250281779