Conformal measures for multidimensional piecewise invertible maps

Conformal measures for multidimensional piecewise invertible maps

Given a piecewise invertible map T : X → X and a weight g : X →]0,∞[, a conformal measure ν is a probability measure on X such that, for all measurable A ⊂ X with T : A→ TA invertible, ν(TA) = λ ∫

Uniqueness of equilibrium measures for countable Markov shifts and multidimensional piecewise expanding maps

We prove that potentials with summable variations on topologically transitive countable Markov shifts have at most one equilibrium measure. We apply this to multidimensional piecewise expanding maps using their Markov diagrams.

Invertible Piecewise Linear Approximations for Color Reproduction

We consider the use of linear splines with variable knots for the approximation of unknown functions from data , motivated by control and estimation problems arising in color systems management. Unlike most popular nonlinear-in-parameters representations, piecewise linear (PL) functions can be simply inverted in closed form. For the one-dimensional case, we present a study comparing P L and neu...

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 ...

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