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<p>We prove strong statistical stability of a large class of one-dimensional maps which may have an arbitrary finite number of non-degenerate critical points and/or singularities, and satisfy some expansion and bounded recurrence conditions. This generalises known results for maps with critical points and bounded derivatives and, in particular, proves statistical stability of Lorenz-like maps with critical points and singularities. We introduce a natural metric on the space of maps with discontinuities which does not seem to have been used before in the literature.</p>

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Statistical Stability of Interval Maps with Critical Points and Singularities

  • 期刊论文

  • 发表日期：

    2025年4月29日

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  • José F. Alves,
  • Dalmi Gama,
  • Stefano Luzzatto

摘要

We prove strong statistical stability of a large class of one-dimensional maps which may have an arbitrary finite number of non-degenerate critical points and/or singularities, and satisfy some expansion and bounded recurrence conditions. This generalises known results for maps with critical points and bounded derivatives and, in particular, proves statistical stability of Lorenz-like maps with critical points and singularities. We introduce a natural metric on the space of maps with discontinuities which does not seem to have been used before in the literature.