Proof of the Pruning Front Conjecture for certain Hénon parameters
arXiv:1112.0705 · doi:10.1088/0951-7715/26/3/679
Abstract
The Pruning Front Conjecture is proved for an open set of Hénon parameters far from unimodal. More specifically, for an open subset of Hénon parameter space, consisting of two connected components one of which intersects the area-preserving locus, it is shown that the associated Hénon maps are prunings of the horseshoe. In particular, their dynamics is a subshift of the two-sided two-shift.
References in corpus (4)
- Henon mappings in the complex domain II: projective and inductive limits of polynomials
- On Loops in the Hyperbolic Locus of the Complex Hénon Map and Their Monodromies
- Complex Horseshoes and the Dynamics of Mappings of Two Complex Variables
- The Henon Family: The Complex Horseshoe Locus and Real Parameter Space