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- W2912643002 abstract "We introduce two Diophantine conditions on rotation numbers of interval exchange maps (i.e.m) and translation surfaces: the emph{absolute Roth type condition} is a weakening of the notion of Roth type i.e.m., while the emph{dual Roth type} condition is a condition on the emph{backward} rotation number of a translation surface. We show that results on the cohomological equation previously proved in cite{MY} for restricted Roth type i.e.m. (on the solvability under finitely many obstructions and the regularity of the solutions) can be extended to restricted emph{absolute} Roth type i.e.m. Under the dual Roth type condition, we associate to a class of functions with emph{subpolynomial} deviations of ergodic averages (corresponding to relative homology classes) emph{distributional} limit shapes, which are constructed in a similar way to the emph{limit shapes} of Birkhoff sums associated in cite{MMY3} to functions which correspond to positive Lyapunov exponents." @default.
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- W2912643002 date "2020-01-01" @default.
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- W2912643002 title "On Roth type conditions, duality and central Birkhoff sums for i.e.m." @default.
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- W2912643002 doi "https://doi.org/10.24033/ast.1111" @default.
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