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Differentiable Dynamical Systems: An Introduction to Structural Stability and Hyperbolicity

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  • Dynamical Systems and Hyperbolicity.
  • Differentiable Dynamical Systems : An Introduction to Structural Stability and Hyperbolicity.
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Dynamical Systems and Hyperbolicity. This process is experimental and the keywords may be updated as the learning algorithm improves. This is a preview of subscription content, log in to check access. Adler, R. Afraimovich, V. International Press, Somerville, MA Andronov, A. SSSR 14 , — Google Scholar. Pergamon Press Springer, Heidelberg Anishchenko, VS.

Tutorial and Modern Development. Springer, Berlin, Heidelberg Anosov, D. Trudy Mat. Steklov 90 , 3— MathSciNet Google Scholar. Sataev, H. Springer, New York Arnold, V. Springer-Verlag, Heidelberg Benjamin, New York Barreira, L. Proceedings of Symposia in Pure Mathematics, pp. AMS Beck, C. Cambridge University Press, Cambridge CrossRef Google Scholar. Benettin, G. Meccanica 15 , 9—30 Birkhoff, G. Bonatti, C. A Global Geometric and Probobalistic Perspective. Encyclopedia of Mathematical Sciences. Springer, Berlin, Heidelberg, New York Bowen R.

Lecture Notes in Math. Coudcnc, Y. Notices of the American Mathematical Society 53 , 8—13 Devaney, R.

Dynamical Systems and Chaos: Fixed Points and Stability Part 1

Westview Press, New York Eckmann, J. Feller, W. Wiley, New York Greene, J. Physica D 24 , — Grines, V. Regular and Chaotic Dynamics 11 2 , — Guckenheimer, J.. Holmes, P. Springer-Verlag, New York Hasselblatt, B.

Pesin theory - Encyclopedia of Mathematics

Schmeling, J. Preprint ESI , Vienna In: Scott, A. Routledge, New York Hilborn, R. Oxford University Press, Cambridge Kaplan, J. In: Peitgen, H. Lecture Notes in Mathematics, , pp. Springer, Berlin, New York Katok, A.

Differentiable Dynamical Systems An Introduction to Structural Stability and Hyperbolicity

Dynamics Reported pp Cite as. The aim of this paper is to show that many of the interesting topological consequences of hyperbolicity follow from just one lemma about exponential dichotomy.


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Our main lemma asserts that there are local stable manifolds and local unstable manifolds associated with a sequence of maps which are close to hyperbolic linear maps, and that certain local stable manifolds and local unstable manifolds have unique points of intersection. Our main lemma also includes detailed estimates for the positions of the local stable and unstable manifolds, and for the behavior of orbits in the local stable and unstable manifolds. This is an exponential dichotomy result because the hypotheses guarantee that orbits diverge either in the forward direction or in the backward direction.

In applications the maps represent a given dynamical system, or dynamical systems in a neighbor hood of a given dynamical system, in local coordinates. Unable to display preview. Download preview PDF. Skip to main content. Advertisement Hide. Hyperbolicity and Exponential Dichotomy for Dynamical Systems.

an introduction to structural stability and hyperbolicity

This process is experimental and the keywords may be updated as the learning algorithm improves. This is a preview of subscription content, log in to check access. Google Scholar. Fenichel, Asymptotic stability with rate conditions, Indiana Univ. J , 23 — Grobman, Homeomorphisms of systems of differential equations, Dokl. Nauk -