Rotation numbers for \(S^2\) diffeomorphisms. (English) Zbl 1385.37059
Katok, Anatole (ed.) et al., Modern theory of dynamical systems. A tribute to Dmitry Victorovich Anosov. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-2560-9/pbk; 978-1-4704-4119-7/ebook). Contemporary Mathematics 692, 101-110 (2017).
Summary: In these notes we describe the properties of, and generalize, the function \(\mathcal {R}\) which assigns a number to a \(4\)-tuple of distinct fixed points of an orientation preserving homeomorphism or diffeomorphism of \(S^2\).
For the entire collection see [Zbl 1370.37002].
For the entire collection see [Zbl 1370.37002].
MSC:
| 37E45 | Rotation numbers and vectors |
| 37C25 | Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics |
| 37E30 | Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces |
References:
| [1] | Milnor, J., Morse theory, Based on lecture notes by M. Spivak and R. Wells. Annals of Mathematics Studies, No. 51, vi+153 pp. (1963), Princeton University Press, Princeton, N.J. · Zbl 0108.10401 |
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