Journal ArticleDOI
On the Stable Manifold Theorem
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This article is published in Bulletin of The London Mathematical Society.The article was published on 1970-07-01. It has received 79 citations till now. The article focuses on the topics: Stable manifold theorem & Invariant manifold.read more
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Book
Asymptotic Behavior of Dissipative Systems
TL;DR: In this article, the authors consider a continuous dynamical system with a global attractor and describe the properties of the flow on the attractor asymptotically smooth and Morse-Smale maps.
Book
Global Stability of Dynamical Systems
TL;DR: In this article, the authors present a Potpourri of stability results for Hyperbolic Sets and Markov Partitions for stable manifolds, as well as a list of notations.
Journal ArticleDOI
Partially hyperbolic dynamical systems
M I Brin,Ja B Pesin +1 more
TL;DR: In this paper, smooth dynamical systems having contracting and expanding invariant foliations (of not necessarily complementary dimensions) are investigated, and the K-property is established for such systems under additional assumptions.
Journal ArticleDOI
The parameterization method for invariant manifolds I: manifolds associated to non-resonant subspaces
TL;DR: In this paper, the authors introduced a method to prove existence of invariant manifolds and to find simple polynomial maps which are congruent to the dynamics on them, and they showed that if X1 is an invariant subspace of A and A satisfies certain spectral properties, then there exists a unique Cr manifold which is invariant under======F and tangent to X1.
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Book ChapterDOI
Differentiable dynamical systems
TL;DR: A survey article on the area of global analysis defined by differentiable dynamical systems or equivalently the action (differentiable) of a Lie group G on a manifold M is presented in this paper.