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- W1981035988 abstract "A rotation number in the case of one-dimensional maps is introduced. As is shown, this rotation number is equivalent to the already known rotation number in the case of two-dimensional maps. The definition of the rotation number is given in two steps. First, it is defined for periodic orbits inside a window of organized motion (WOM). We show that in this case our definition coincides with the definition of the over-rotation number. Then, our definition is further generalized for chaotic orbits outside the WOMs. Thus, we obtain a unified definition of the rotation number for the whole area of the chaotic zone of the bifurcation diagram, having a number of useful applications. Namely, it can be used as a tool to distinguish whether an orbit is contained within a WOM or not, as a tool of numerical location of the bifurcation points, of the band mergings, as well as of the boundary points of a WOM. Finally, a method of numerical calculation of the percentage of the cumulative width of the WOMs in every particular segment (chaotic band) of the chaotic zone is given." @default.
- W1981035988 created "2016-06-24" @default.
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- W1981035988 date "2006-11-21" @default.
- W1981035988 modified "2023-09-27" @default.
- W1981035988 title "The rotation number in one-dimensional maps: definition and applications" @default.
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- W1981035988 doi "https://doi.org/10.1088/0305-4470/39/49/011" @default.
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