Anosov flows and expansiveness
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- by Victor Norton and Thomas O’Brien PDF
- Proc. Amer. Math. Soc. 40 (1973), 625-628 Request permission
Abstract:
We prove that an Anosov diffeomorphism of a compact manifold is expansive. We also show that a continuous flow on an infinite compact metric space cannot be expansive. We define a corresponding expansive concept for flows, that of an unstable flow (the word unstable is used here in a Lyapunov sense). We then prove that Anosov flows of compact manifolds are unstable.References
- Serge Lang, Introduction to differentiable manifolds, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0155257
- Thomas O’Brien and William Reddy, Each compact orientable surface of positive genus admits an expansive homeomorphism, Pacific J. Math. 35 (1970), 737–741. MR 276953
- S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747–817. MR 228014, DOI 10.1090/S0002-9904-1967-11798-1
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 40 (1973), 625-628
- MSC: Primary 58F15
- DOI: https://doi.org/10.1090/S0002-9939-1973-0322907-X
- MathSciNet review: 0322907