Hyperbolic Sets

Michael Shub
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Michael Shub: IBM, Thomas J. Watson Research Center

Chapter Chapter 4 in Global Stability of Dynamical Systems, 1987, pp 20-32 from Springer

Abstract: Abstract Let Λ be an invariant set for a C r diffeomorphism f of a manifold M. We say that Λ is a hyperbolic set for f if there is a continuous splitting of the tangent bundle of M restricted to Λ, TM Λ, which is Tf invariant: $$T{M_\Lambda } = {E^s} \oplus {E^u};\;Tf\left( {{E^s}} \right) = {E^s};\;Tf\left( {{E^u}} \right) = {E^u};$$ and for which there are constants c and λ, c>0 and 0

Keywords: Periodic Orbit; Periodic Point; Global Stability; Finite Sequence; Vertical Band (search for similar items in EconPapers)
Date: 1987
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DOI: 10.1007/978-1-4757-1947-5_4

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