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]).
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© 1992 Springer Science+Business Media New York
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Wiggins, S. (1992). Markov Models. In: Chaotic Transport in Dynamical Systems. Interdisciplinary Applied Mathematics, vol 2. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3896-4_5
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DOI: https://doi.org/10.1007/978-1-4757-3896-4_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3096-5
Online ISBN: 978-1-4757-3896-4
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