On the growth rate inequality for periodic points in the two sphere. (English) Zbl 1450.37019
Summary: In this article we find a condition implying that the growth of the number of \(n\)-periodic points of a degree \(d\) map of the two-sphere is exponential with rate \(\log |d|\). This generalizes previous results on this matter.
MSC:
| 37C25 | Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics |
| 37E20 | Universality and renormalization of dynamical systems |
| 37C35 | Orbit growth in dynamical systems |
| 37C05 | Dynamical systems involving smooth mappings and diffeomorphisms |
| 37B20 | Notions of recurrence and recurrent behavior in topological dynamical systems |
Keywords:
topological dynamics; low-dimensional dynamical systems; growth rate inequality; Lefschetz’s indexReferences:
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