A metric property of period doubling for nonisosceles trapezoidal maps on an interval (Q1096942)

This paper considers some bifurcation properties related to a class of real one-dimensional maps defined by a piecewise linear function having a nonisosceles trapezoidal representation, and depending on a parameter. More precisely, it is a matter of proving that the parameter bifurcation values, leading to period doubling (Myrberg's spectrum, or Myrberg's cascade), are quadratically convergent to a limit point (Myrberg singular value of the first type). So the authors generalize a result obtained previously by Beyer and Stein (1982) in the isosceles trapezoidal case, and which is based in part on numerical work. Here a proof, not involving estimates obtained by computer, is given.