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- W1934400137 abstract "For a dynamical system $(X,T)$ and function $f:Xto mathbb {R}^d$ we consider the corresponding generalised rotation set. This is the convex subset of $mathbb {R}^d$ consisting of all integrals of $f$ with respect to $T$-invariant probability measures. We study the entropy $H(varrho )$ of rotation vectors $varrho$, and relate this to the directional entropy $mathcal {H}(varrho )$ of Geller & Misiurewicz. For $(X,T)$ a mixing subshift of finite type, and $f$ of summable variation, we prove that if the rotation set is strictly convex then the functions $mathcal {H}$ and $H$ are in fact one and the same. For those rotation sets which are not strictly convex we prove that $mathcal {H}(varrho )$ and $H(varrho )$ can differ only at non-exposed boundary points $varrho$." @default.
- W1934400137 created "2016-06-24" @default.
- W1934400137 creator A5075520450 @default.
- W1934400137 date "2001-04-18" @default.
- W1934400137 modified "2023-09-25" @default.
- W1934400137 title "Rotation, entropy, and equilibrium states" @default.
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- W1934400137 doi "https://doi.org/10.1090/s0002-9947-01-02706-4" @default.
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