MacKay et al. [1984, 1987] and Meiss and Ott  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 ) and Camassa (see Camassa and Wiggins ).
KeywordsVortex Convection Manifold
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