Abstract
We construct a plethora of Anosov–Katok diffeomorphisms with non-ergodic generic measures and various other mixing and topological properties. We also construct an explicit collection of the set containing the generic points of the system with interesting values of its Hausdorff dimension.
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Notes
\(\varepsilon _n^{(1)} \varepsilon _n^{(2)}, \varepsilon _n^{(3)}\) and \(\varepsilon _n^{(4)}\) are just notations of different parameters, not related by any power of \(\varepsilon _n^{(1)}\).
We refer to the map \(\tilde{\phi }_n\) as a permutation map because it rearranges the elements of the partition.
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Acknowledgements
The author wants to thank P. Kunde and S. Banerjee for suggesting the problem and for valuable discussions which helped to develop the ideas put forward. The author wants to thank to the reviewer for their insightful comments and constructive feedback, which greatly contributed to the enhancement of this work.
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The work was supported by the University Grants Commission (UGC-JRF), India.
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Khurana, D. Smooth Anosov Katok Diffeomorphisms with Generic Measure. J Dyn Diff Equat (2023). https://doi.org/10.1007/s10884-023-10313-y
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DOI: https://doi.org/10.1007/s10884-023-10313-y