Markov Models

  • Stephen Wiggins
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 2)

Abstract

MacKay et al. [1984, 1987] and Meiss and Ott [1986] were the first to consider transport between regions in phase space separated by partial barriers such as cantori and segments of stable and unstable manifolds of periodic orbits of two-dimensional, area-preserving maps. They proposed a model for transport which requires certain assumptions on the underlying dynamics that result in a description of transport as a Markov process. In this chapter we will describe the Markov model of Mackay, Meiss, Ott, and Percival and compare it with the exact methods for two-dimensional area-preserving maps developed by Rom-Kedar and Wiggins and described in Chapter 2. The material in this chapter is derived from joint work with Rom-Kedar (see Rom-Kedar and Wiggins [1990]) and Camassa (see Camassa and Wiggins [1991]).

Keywords

Vortex Convection Manifold 

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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Stephen Wiggins
    • 1
  1. 1.Applied Mechanics DepartmentCalifornia Institute of TechnolgyPasadenaUSA

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