Rotation intervals of endomorphisms of the circle. (English) Zbl 0605.58027
The rotation number of a diffeomorphism \(f: S^ 1\to S^ 1\), with lift \(F: {\mathbb{R}}\to {\mathbb{R}}\) is defined as \(\lim_{n\to \infty}(F^ n(x)- x)/n\). We investigate the case where f is an endomorphism. Then this limit may not exist and may depend on x. We investigate the set of limit points of \((F^ n(x)-x)/n\), \(n\to \infty\), as a function of x.
MSC:
| 37D15 | Morse-Smale systems |
References:
| [1] | Ito, Math. Proc. Camb. Phil. Soc. 89 pp 107– (1981) |
| [2] | Newhouse, IHES Publ. Math. 57 pp 5– (1983) · Zbl 0518.58031 · doi:10.1007/BF02698773 |
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