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<p>In our previous work (Kiriki, S., Li, X., Nakano, Y., Soma, T in Comm. Math. Phys. 1241–1269 (2022)), we proved the existence of observable Lyapunov irregular sets for a class of surface diffeomorphisms. This correction addresses a gap in the proof of Lemma 4.5 of that paper, which arose from an oversight in applying an estimate. We rectify this by adjusting the initial setup, including the conditions on the diffeomorphism and the definitions of related sequences. These modifications secure the proof of Lemma 4.5 and, consequently, reinforce the main results of (Kiriki, S., Li, X., Nakano, Y., Soma, T in Comm. Math. Phys. 1241–1269 (2022)).</p>

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Correction to: Abundance of Observable Lyapunov Irregular Sets

  • 期刊论文

  • 发表日期：

    2026年5月2日

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  • Shin Kiriki,
  • Xiaolong Li,
  • Yushi Nakano,
  • Teruhiko Soma

摘要

In our previous work (Kiriki, S., Li, X., Nakano, Y., Soma, T in Comm. Math. Phys. 1241–1269 (2022)), we proved the existence of observable Lyapunov irregular sets for a class of surface diffeomorphisms. This correction addresses a gap in the proof of Lemma 4.5 of that paper, which arose from an oversight in applying an estimate. We rectify this by adjusting the initial setup, including the conditions on the diffeomorphism and the definitions of related sequences. These modifications secure the proof of Lemma 4.5 and, consequently, reinforce the main results of (Kiriki, S., Li, X., Nakano, Y., Soma, T in Comm. Math. Phys. 1241–1269 (2022)).