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Research Article | Open Access

The finiteness of a certain class of geometric ergodic measures

School of Mathematics, Nanjing University, Nanjing 210093, China
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Abstract

From the perspective of the dominated splitting, under certain assumptions, there existed finitely many closed sets A 1 , A 2 , … , A m (with A i ≠ A j for i ≠ j) such that the support of any ergodic geometric measure coincided with one of them.

Keywords

dominated splittinggeometric measureC1-topology
CLC number: 37D30, 37C40, 37D25, 37D35

References

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AIMS Mathematics
Volume 11 Issue 6,
June 2026
Pages 16602-16612
DOI: 10.3934/math.2026681

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Zhang H. The finiteness of a certain class of geometric ergodic measures. AIMS Mathematics, 2026, 11(6): 16602-16612. https://doi.org/10.3934/math.2026681

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Received: 13 April 2026
Revised: 30 May 2026
Accepted: 05 June 2026
Published: 15 June 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)