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Hausdorff Dimension of Invariant Subsets for Endomorphisms of the Circle with an Indifferent Fixed Point
Author(s) -
Urbański M.
Publication year - 1989
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-40.1.158
Subject(s) - mathematics , endomorphism , invariant (physics) , hausdorff dimension , fixed point , ergodic theory , invariant measure , conformal map , combinatorics , pure mathematics , discrete mathematics , mathematical analysis , mathematical physics
A class of maps T of the circle S 1 with an indifferent fixed point is studied. It is proved that for every 0 ⩽ t < 1 there exists a closed T ‐invariant subset X of S 1 and an ergodic probability invariant measure μ such that HD ( X ) = HD (μ) = t . The set of conformal measures for T is also investigated.
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