Stable and Unstable Manifolds

Thomas S. Parker and Leon O. Chua
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Thomas S. Parker: Hewlett Packard
Leon O. Chua: University of California, Department of Electrical Engineering and Computer Sciences

Chapter Chapter 6 in Practical Numerical Algorithms for Chaotic Systems, 1989, pp 139-166 from Springer

Abstract: Abstract In this chapter, we discuss the stable and unstable manifolds of an equilibrium point and of a fixed point. Stable and unstable manifolds are a useful tool for both the theorist and the simulator of nonlinear systems. As we shall see, under the proper conditions, the structure of the manifolds indicates the presence of Smale horseshoes which, in turn, implies sensitive dependence on initial conditions.

Keywords: Equilibrium Point; Unstable Manifold; Homoclinic Orbit; Stable Manifold; Librium Point (search for similar items in EconPapers)
Date: 1989
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-3486-9_6

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DOI: 10.1007/978-1-4612-3486-9_6

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