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- W2096804511 abstract "Abstract Given an orientation preserving C 2 expanding mapping g : S 1 → S l of a circle we consider the family of closed invariant sets K g (ε) defined as those points whose forward trajectory avoids the interval (0, ε). We prove that topological entropy of g | K g (ε) is a Cantor function of ε. If we consider the map g ( z ) = z q then the Hausdorff dimension of the corresponding Cantor set around a parameter ε in the space of parameters is equal to the Hausdorff dimension of K g (ε). In § 3 we establish some relationships between the mappings g | K g (ε) and the theory of β-transformations, and in the last section we consider DE-bifurcations related to the sets K g (ε)." @default.
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- W2096804511 date "1986-06-01" @default.
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- W2096804511 title "On Hausdorff dimension of invariant sets for expanding maps of a circle" @default.
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- W2096804511 doi "https://doi.org/10.1017/s0143385700003461" @default.
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