Solenoidal attractors with bounded combinatorics are shy

Abstract

We show that in a generic finite-dimensional real-analytic family of real-analytic multimodal maps, the subset of parameters on which the corresponding map has a solenoidal attractor with bounded combinatorics is a set with zero Lebesgue measure.

66 pages, 3 figures

Cited by in corpus (4)

• Asymmetric unimodal maps with non-universal period-doubling scaling laws
• Shy shadows of infinite-dimensional partially hyperbolic invariant sets
• The boundary of chaos for interval mappings
• Renormalization of symmetric bimodal maps with low smoothness