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.

Authors

Daniel Smania

Departamento de Matemática, Instituto de Ciências Matemáticas e de Computaçāo, Universidade de São Paulo-Campus de São Carlos (ICMC/USP/São Carlos), Caixa Postal 668, CEP 13560-970, São Carlos-SP, Brazil