The finiteness of a certain class of geometric ergodic measures

Hangyue Zhang; Hangyue Zhang

doi:10.3934/math.2026681

AIMS Mathematics

2026, Volume 11, Issue 6: 16602-16612. doi: 10.3934/math.2026681

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The finiteness of a certain class of geometric ergodic measures

Hangyue Zhang ^,

School of Mathematics, Nanjing University, Nanjing 210093, China

Received: 13 April 2026 Revised: 30 May 2026 Accepted: 05 June 2026 Published: 10 June 2026
MSC : 37D30, 37C40, 37D25, 37D35

From the perspective of the dominated splitting, under certain assumptions, there existed finitely many closed sets $ A_1, A_2, \dots, A_m $ (with $ A_i \neq A_j $ for $ i \neq j $) such that the support of any ergodic geometric measure coincided with one of them.
- dominated splitting,
- geometric measure,
- $ C^1 $-topology
Citation: Hangyue Zhang. The finiteness of a certain class of geometric ergodic measures[J]. AIMS Mathematics, 2026, 11(6): 16602-16612. doi: 10.3934/math.2026681

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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, \dots, A_m $ (with $ A_i \neq A_j $ for $ i \neq j $) such that the support of any ergodic geometric measure coincided with one of them.

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