Inducing, slopes, and conjugacy classes

1994/03/05 by Roza Galeeva, Marco Martens, Galeeva, Roza +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.math/9403221

arxiv created 1994/03/05 · arxiv updated 2009/11/30

Abstract

We show that the conjugacy class of an eventually expanding continuous piecewise affine interval map is contained in a smooth codimension 1 submanifold of parameter space. In particular conjugacy classes have empty interior. This is based on a study of the relation between induced Markov maps and ergodic theoretical behavior.

Related

• Invariable generation of certain groups of piecewise linear homeomorphisms of the interval
• Robust and generic properties for piecewise continuous maps on the interval
• Semiconjugacy to a map of a constant slope
• Interval maps quasi-symmetrically conjugated to a piecewise affine map
• Smooth rigidity for very non-algebraic expanding maps