Advanced Studies in Pure Mathematics

Pattern formation from projectively dynamical systems and iterations by families of maps

Tsuyoshi Kato

Full-text: Open access

Abstract

In this paper we describe and formulate dynamical pattern formation, which is given by hierarchies of dynamical systems by scale transform. They arise from random iterations by maps and create PDE such as KdV or Lotka Volterra. As an intermediate scale, we use tropical geometry.

Article information

Source
Probabilistic Approach to Geometry, M. Kotani, M. Hino and T. Kumagai, eds. (Tokyo: Mathematical Society of Japan, 2010), 243-262

Dates
Received: 7 December 2008
Revised: 21 June 2009
First available in Project Euclid: 24 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543086322

Digital Object Identifier
doi:10.2969/aspm/05710243

Mathematical Reviews number (MathSciNet)
MR2648263

Zentralblatt MATH identifier
1252.37059

Subjects
Primary: 37E 39A

Keywords
Scale transform Tropical geometry discrete dynamical systems

Citation

Kato, Tsuyoshi. Pattern formation from projectively dynamical systems and iterations by families of maps. Probabilistic Approach to Geometry, 243--262, Mathematical Society of Japan, Tokyo, Japan, 2010. doi:10.2969/aspm/05710243. https://projecteuclid.org/euclid.aspm/1543086322


Export citation