Complexity geometry and Schwarzian dynamics

Fractals in complexity and geometry

Relative Kolmogorov complexity and geometry

We use the connection of Hausdorff dimension and Kolmogorov complexity to describe a geometry on the Cantor set including concepts of angle, projections and scalar multiplication. A question related to compressibility is addressed using these geometrical ideas.

Dynamics of Functions with an Eventual Negative Schwarzian Derivative

In the study of one dimensional dynamical systems one often assumes that the functions involved have a negative Schwarzian derivative. In this paper we consider a generalization of this condition. Specifically, we consider the interval functions of a real variable having some iterate with a negative Schwarzian derivative and show that many known results generalize to this larger class of functi...

Lorentzian Worldlines and Schwarzian Derivative

The aim of this note is to relate the classical Schwarzian derivative and the geometry of Lorentz surfaces of constant curvature. 1. The starting point of our investigations lies in the following remark (joint work with L. Guieu). Consider a curve y = f(x) in the Lorentz plane with metric g = dxdy. If f (x) > 0, then its Lorentz curvature can be computed : ̺(x) = f (x) (f (x)) and enjoys the qui...

Cinderella: Computation, complexity, geometry

With Cinderella[12], you can easily create constructions, figures consisting of points, lines, circles, conics and other geometric elements, together with relations that describe the mathematical connections between the elements.[5] A standard example is a triangle, consisting of three points and three segments connecting each pair of points, and the altitudes in that triangle. The representati...