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Construction and applications of proximal maps for typical cocycles
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Construction and applications of proximal maps for typical cocycles
classification
math.DS
keywords
orbitcocyclesgivenperiodicproximalsegmenttypicalalong
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For typical cocycles over subshifts of finite type, we show that for any given orbit segment, we can construct a periodic orbit such that it shadows the given orbit segment and that the product of the cocycle along its orbit is a proximal linear map. Using this result, we show that suitable assumptions on the periodic orbits have consequences over the entire subshift.
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