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Measures of maximal and full dimension for smooth maps
Part of:
Infinite-dimensional dissipative dynamical systems
Smooth dynamical systems: general theory
Dynamical systems with hyperbolic behavior
Published online by Cambridge University Press: 17 March 2023
Abstract
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.
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