Piecewise smoothness of conjugate homeomorphisms of a circle with corners (Q1567807)

The paper deals with dynamical properties of circle homeomorphisms with corners, that is maps that are smooth everywhere except several singularities where the first derivative is discontinuous. The author considers the orientation-preserving homeomorphism \(T_fx\) of the unit circle, \[ T_fx= \{f(x)\}_f, \qquad x\in S^1= [0,1), \] where the braces denote the fractional part of a number and \(f(x)\) is a pullback determining \(T_f\). Under some natural conditions on \(f\), he studies the renormalization group behaviour and proves its convergence to linear transformations.