Continuous SL(d,R) cocycles over positive-entropy subshifts of finite type either admit a dominated splitting or can be C0-approximated to C^α-stably support positive-entropy ergodic measures on bounded orbits.
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A survey that reviews Borel hierarchy and four representations of Cantor sets, gives explicit descriptions for thin zero-measure and positive-measure families, shows the middle-third set belongs to all three families, and isolates open problems.
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Cocycles with Quasi-Conformality II: Ergodic measures with positive entropy
Continuous SL(d,R) cocycles over positive-entropy subshifts of finite type either admit a dominated splitting or can be C0-approximated to C^α-stably support positive-entropy ergodic measures on bounded orbits.
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Descriptions of Cantor Sets: A Set-Theoretic Survey and Open Problems
A survey that reviews Borel hierarchy and four representations of Cantor sets, gives explicit descriptions for thin zero-measure and positive-measure families, shows the middle-third set belongs to all three families, and isolates open problems.