Computability and complexity of Julia sets: a review - Kota, Hiratsuka; Yuzuru, Sato; Zin, Arai
Since A. M. Turing introduced the notion of computability
in 1936, various theories of real number computation have been
studied. Some are of interest in nonlinear and statistical
physics while others are extensions of the mathematical theory
of computation. In this review paper, we introduce a recently developed computability theory for Julia sets in complex dynamical systems by Braverman and Yampolsky.
Global Solvability of Constrained Singular Diffusion Equation Associated with Essential Variation - Giga, Yoshikazu; Kuroda, Hirotoshi; Yamazaki, Noriaki
We consider a gradient flow system of total variation with constraint.
Our system is often used in the color image processing to remove a
noise from picture. In particular, we want to preserve the sharp edges of picture
and color chromaticity. Therefore, the values of solutions to our model is
constrained in some fixed compact Riemannian manifold. By this reason, it is
very difficult to analyze such a problem, mathematically. The main object of
this paper is to show the global solvability of a constrained singular diffusion
equation associated with total variation. In fact, by using abstract convergence
theory of convex functions, we shall prove the existence of...