Convex dynamics and applications
| Autor: | Roy L. Adler, Bruce Kitchens, Marco Martens, Charles Tresser, Michael Shub, Charles Pugh |
|---|---|
| Přispěvatelé: | Faculty of Science and Engineering |
| Jazyk: | angličtina |
| Rok vydání: | 2005 |
| Předmět: |
General Mathematics
Symbolic dynamics ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION 0102 computer and information sciences Dynamical Systems (math.DS) Diophantine approximation Dynamical system 01 natural sciences Corollary FOS: Mathematics Mathematics - Dynamical Systems 0101 mathematics 37Cxx 34Dxx Mathematics ComputingMethodologies_COMPUTERGRAPHICS Discrete mathematics SETS business.industry Applied Mathematics 010102 general mathematics Regular polygon Algebra Areas of mathematics 010201 computation theory & mathematics Piecewise Digital printing business |
| Zdroj: | Ergodic Theory and Dynamical Systems, 25, 321-352 |
| ISSN: | 0143-3857 |
| DOI: | 10.1017/s0143385704000537 |
| Popis: | This paper proves a theorem about bounding orbits of a time dependent dynamical system. The maps that are involved are examples in convex dynamics, by which we mean the dynamics of piecewise isometries where the pieces are convex. The theorem came to the attention of the authors in connection with the problem of digital halftoning. \textit{Digital halftoning} is a family of printing technologies for getting full color images from only a few different colors deposited at dots all of the same size. The simplest version consist in obtaining grey scale images from only black and white dots. A corollary of the theorem is that for \textit{error diffusion}, one of the methods of digital halftoning, averages of colors of the printed dots converge to averages of the colors taken from the same dots of the actual images. Digital printing is a special case of a much wider class of scheduling problems to which the theorem applies. Convex dynamics has roots in classical areas of mathematics such as symbolic dynamics, Diophantine approximation, and the theory of uniform distributions. Comment: LaTex with 9 PostScript figures |
| Databáze: | OpenAIRE |
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