Periodic points for piecewise monotonic transformations

Learning Monotonic Transformations for Classification

A discriminative method is proposed for learning monotonic transformations of the training data while jointly estimating a large-margin classifier. In many domains such as document classification, image histogram classification and gene microarray experiments, fixed monotonic transformations can be useful as a preprocessing step. However, most classifiers only explore these transformations thro...

Piecewise monotone maps without periodic points : Rigidity , measures and complexity

We consider piecewise monotone maps of the interval with zero entropy or no periodic points. First, we give a rigid model for these maps: the interval translations mappings, possibly with ips. It follows, e.g., that the complexity of a piecewise monotone map of the interval is at most polynomial if and only if this map has a nite number of periodic points up to monotone equivalence. Second, we ...

ON THE EXISTENCE OF INVARIANT MEASURES FOR PIECEWISE MONOTONIC TRANSFORMATIONS ( l ) BY A . LASOTA AND

A class of piecewise continuous, piecewise C transformations on the interval [O, l] is shown to have absolutely continuous invariant measures.

Piecewise monotone maps without periodic points: Rigidity, measures and complexity.

Fredholm Determinant for Piecewise Linear Transformations

We call the number ξ the lower Lyapunov number. We will study Spec^) , the spectrum of P \BV> the restriction of P to the subspace BV of functions with bounded variation. The generating function of P is determined by the orbits of the division points of the partition, and the orbits are characterized by a finite dimensional matrix Φ(z) which is defined by a renewal equation (§ 3). Hence, we can...