Abstract
In Chapter 3 we showed that the set consisting of a hyperbolic fixed point of a diffeomorphism and an associated transversal homoclinic orbit is hyperbolic. In this chapter we use symbolic dynamics to describe all the orbits in a neighbourhood of this set. In particular, we shall show that the dynamics in such a neighbourhood is chaotic. Our main tool in establishing the symbolic dynamics is the shadowing theorem (Theorem 4.3).
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© 2000 Springer Science+Business Media Dordrecht
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Palmer, K. (2000). Symbolic Dynamics Near a Transversal Homoclinic Point of a Diffeomorphism. In: Shadowing in Dynamical Systems. Mathematics and Its Applications, vol 501. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3210-8_5
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DOI: https://doi.org/10.1007/978-1-4757-3210-8_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4827-4
Online ISBN: 978-1-4757-3210-8
eBook Packages: Springer Book Archive