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<p>In this paper, we count the number of Pollicott–Ruelle resonances for open hyperbolic systems and Axiom A flows. In particular, we prove polynomial upper bounds and sublinear lower bounds on the number of resonances with modulus less than <i>r</i> in strips for open hyperbolic systems and Axiom A flows with a transversality condition.</p>

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Counting Pollicott–Ruelle Resonances for Axiom A Flows

  • 期刊论文

  • 发表日期：

    2025年1月11日

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  • Long Jin,
  • Zhongkai Tao

摘要

In this paper, we count the number of Pollicott–Ruelle resonances for open hyperbolic systems and Axiom A flows. In particular, we prove polynomial upper bounds and sublinear lower bounds on the number of resonances with modulus less than r in strips for open hyperbolic systems and Axiom A flows with a transversality condition.