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measure of full dimension

Ergodic Theory and Dynamical Systems (1)

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Measures of maximal and full dimension for smooth maps
Part of
YURONG CHEN, CHIYI LUO, YUN ZHAO
Journal:

Ergodic Theory and Dynamical Systems / Volume 44 / Issue 1 / January 2024

Published online by Cambridge University Press:

17 March 2023, pp. 31-49

Print publication:

January 2024
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For a $C^1$ non-conformal repeller, this paper proves that there exists an ergodic measure of full Carathéodory singular dimension. For an average conformal hyperbolic set of a $C^1$ diffeomorphism, this paper constructs a Borel probability measure (with support strictly inside the repeller) of full Hausdorff dimension. If the average conformal hyperbolic set is of a $C^{1+\alpha }$ diffeomorphism, this paper shows that there exists an ergodic measure of maximal dimension.