Sylvie Oliffson Kamphorst

On the fractal dimension of self-affine profiles

One-dimensional profiles f(x) can be characterized by a Minkowski-Bouligand dimension D and by a scale-dependent generalized roughness W(f, epsilon ). This roughness can be defined as the dispersion around a chosen fit to f(x) in an epsilon -scale. It is shown that D=limepsilon to 0(2-In W(f, epsilon )/In epsilon ) holds for profiles nowhere differentiable. This establishes a close connection between the roughness and the fractal dimension and proves that D=2-H for self-affine profiles (H is the roughness or Hurst exponent). Two numerical algorithms based on the roughness, one around the local average (f(x))epsilon (usual roughness) and the other around the local RMS straight line (a generalized roughness), are discussed. The estimates of D for standard self-affine profiles are reliable and robust, especially for the last method.

Chaotic Properties of the Elliptical Stadium

AbstractThe elliptical stadium is a curve constructed by joining two half-ellipses, with half axesa>1 andb=1, by two straight segments of equal length 2h.Donnay [6] has shown that if 1 <a <

STATIC AND TIME-DEPENDENT PERTURBATIONS OF THE CLASSICAL ELLIPTICAL BILLIARD

\sqrt 2

Time-dependent billiards

and ifh is big enough, then the corresponding billiard map has a positive Lyapunov exponent almost everywhere; moreover,h→∞ asa→

The first Birkhoff coefficient and the stability of 2-periodic orbits on billiards

\sqrt 2

Oscilações em reações autocatalíticas cúbicas

In this work we prove that if