Abstract
The goal in this chapter is to generalize many of the concepts developed in the previous chapters for lower-dimensional dynamical systems to higher dimensions. We will consider only Hamiltonian systems, although further generalizations to non-Hamiltonian systems are possible (these will be briefly discussed later). We will begin by considering the types of structures that can arise in the phase space of a Hamiltonian system and the potential of these structures for providing barriers to transport. In particular, we are looking for an appropriate generalization of the notion of a “separatrix” to higher dimensions. First, however, let us consider the essential characteristics that define what we mean by the term “separatrix.”
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© 1992 Springer Science+Business Media New York
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Wiggins, S. (1992). Transport in к-Degree-of-Freedom Hamiltonian Systems, 3 ≤ к < ∞: The Generalization of Separatrices to Higher Dimensions and Their Geometrical Structure. 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_6
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DOI: https://doi.org/10.1007/978-1-4757-3896-4_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3096-5
Online ISBN: 978-1-4757-3896-4
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