Abstract
Up till now our only examples of hyperbolic sets have been hyperbolic fixed points and periodic orbits. In this chapter we give an example of a hyperbolic set which is infinite. Moreover, even though the set consists of only two distinct orbits, we shall show in Chapter 5 that in its neighbourhood the diffeomorphism has chaotic dynamics.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Palmer, K. (2000). Transversal Homoclinic Points of Diffeomorphisms and Hyperbolic Sets. In: Shadowing in Dynamical Systems. Mathematics and Its Applications, vol 501. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3210-8_3
Download citation
DOI: https://doi.org/10.1007/978-1-4757-3210-8_3
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4827-4
Online ISBN: 978-1-4757-3210-8
eBook Packages: Springer Book Archive