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- W4288640983 abstract "For a continuous map on a topological graph containing a loop $S$ it is possible to define the degree (with respect to the loop $S$) and, for a map of degree $1$, rotation numbers. We study the rotation set of these maps and the periods of periodic points having a given rotation number. We show that, if the graph has a single loop $S$ then the set of rotation numbers of points in $S$ has some properties similar to the rotation set of a circle map; in particular it is a compact interval and for every rational $alpha$ in this interval there exists a periodic point of rotation number $alpha$. For a special class of maps called combed maps, the rotation set displays the same nice properties as the continuous degree one circle maps." @default.
- W4288640983 created "2022-07-30" @default.
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- W4288640983 date "2019-01-06" @default.
- W4288640983 modified "2023-10-16" @default.
- W4288640983 title "Rotation sets for graph maps of degree 1" @default.
- W4288640983 doi "https://doi.org/10.48550/arxiv.1901.01524" @default.
- W4288640983 hasPublicationYear "2019" @default.
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