Transversal Homoclinic Points of Diffeomorphisms and Hyperbolic Sets
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.
KeywordsSaddle Point Unstable Manifold Implicit Function Theorem Homoclinic Orbit Exponential Dichotomy
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