Invariant measures for typical quadratic maps

1996/06/15 by Marco Martens, Martens, Marco, Tomasz Nowicki +1
Mathematics · #Mathematical Dynamics and Fractals #Geometric and Algebraic Topology #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.math/9606220

Abstract

A sufficient geometrical condition for the existence of absolutely continuous invariant probability measures for S-unimodal maps will be discussed. The Lebesgue typical existence of such measures in the quadratic family will be a consequence.

Related

• Absolutely Continuous Invariant Measures of Piecewise Linear Lorenz Maps
• Invariant measures for random piecewise convex maps
• New existence theorems in measure theory and equivalence results for the existence of invariant probabilities
• Analyticity of the SRB measure for holomorphic families of quadratic-like Collet-Eckmann maps
• Invariant Probability Measures under p-adic Transformations