Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Probabilistic Approach to Geometry, M. Kotani, M. Hino and T. Kumagai, eds. (Tokyo: Mathematical Society of Japan, 2010), 243 - 262
Pattern formation from projectively dynamical systems and iterations by families of maps
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.
Received: 7 December 2008
Revised: 21 June 2009
First available in Project Euclid: 24 November 2018
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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