Local dimension for piecewise monotonic maps on the interval
1995 ◽
Vol 15
(6)
◽
pp. 1119-1142
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Keyword(s):
AbstractThe local dimension of invariant and conformal measures for piecewise monotonic transformations on the interval is considered. For ergodic invariant measures m with positive characteristic exponent χm we show that the local dimension exists almost everywhere and equals hm/χm For certain conformal measures we show a relation between a pressure function and the Hausdorff dimension of sets, on which the local dimension is constant.
2001 ◽
Vol 63
(3)
◽
pp. 721-734
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2000 ◽
Vol 20
(5)
◽
pp. 1423-1447
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2012 ◽
Vol 391
(1)
◽
pp. 298-311
◽
1965 ◽
Vol 61
(3)
◽
pp. 679-694
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Keyword(s):