Differentiable Dynamical Systems

Steve Smale
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Steve Smale: University of California at Berkeley, Department of Mathematics

A chapter in The Mathematics of Time, 1980, pp 1-82 from Springer

Abstract: Abstract This is 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. An action is a homomorphism G→Diff(M) such that the induced map G×M→M is differentiable. Here Diff(M) is the group of all diffeomorphisms of M and a diffeo- morphism is a differentiable map with a differentiable inverse. Everything will be discussed here from the C ∞ or C r point of view. All manifolds maps, etc. will be differentiable (C r , 1 ≦ r ≦ ∞) unless stated otherwise.

Keywords: Zeta Function; Periodic Point; Stable Manifold; Closed Orbit; Topological Entropy (search for similar items in EconPapers)
Date: 1980
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-8101-3_1

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DOI: 10.1007/978-1-4613-8101-3_1

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