Displaying similar documents to “Some examples of nonsingular Morse-Smale vector fields on S 3 ”

Some examples of vector fields on the 3-sphere

F. Wesley Wilson (1970)

Annales de l'institut Fourier

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Let S 3 denote the set of points with modulus one in euclidean 4-space R 4  ; and let Γ 0 1 ( S 3 ) denote the space of nonsingular vector fields on S 3 with the C 1 topology. Under what conditions are two elements from Γ 0 1 ( S 3 ) homotopic ? There are several examples of nonsingular vector fields on S 3 . However, they are all homotopic to the tangent fields of the fibrations of S 3 due to H. Hopf (there are two such classes). We construct some new examples of vector fields which can be classified geometrically....

On a generalization of the Conley index

Marian Mrozek, James Reineck, Roman Srzednicki (1999)

Banach Center Publications

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In this note we present the main ideas of the theory of the Conley index over a base space introduced in the papers [7, 8]. The theory arised as an attempt to solve two questions concerning the classical Conley index. In the definition of the index, the exit set of an isolating neighborhood is collapsed to a point. Some information is lost on this collapse. In particular, topological information about how a set sits in the phase space is lost. The first question addressed is how to retain...

Periods of Morse-Smale diffeomorphisms of 𝕊²

Juan Luis García Guirao, Jaume Llibre (2008)

Colloquium Mathematicae

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The aim of this paper is to describe the set of periods of a Morse-Smale diffeomorphism of the two-dimensional sphere according to its homotopy class. The main tool for proving this is the Lefschetz fixed point theory.

The Conley index in Hilbert spaces and its applications

K. Gęba, M. Izydorek, A. Pruszko (1999)

Studia Mathematica

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We present a generalization of the classical Conley index defined for flows on locally compact spaces to flows on an infinite-dimensional real Hilbert space H generated by vector fields of the form f: H → H, f(x) = Lx + K(x), where L: H → H is a bounded linear operator satisfying some technical assumptions and K is a completely continuous perturbation. Simple examples are presented to show how this new invariant can be applied in searching critical points of strongly indefinite functionals...