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Abstract <p> We consider a class of gradient-like diffeomorphisms of closed surfaces with negative Euler characteristic. It is shown that all such identity-isotopic diffeomorphisms are connected by a stable arc (containing finitely many saddle-node bifurcations). This result is contrast with the stable classification of gradient-like diffeomorphisms of the 2-sphere or the 2-torus, according to which the set of identity-isotopic diffeomorphisms on such surfaces is divided into a countable number of stable connectivity classes. </p>

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Stable Connectivity of Identity-Isotopic Gradient-Like Diffeomorphisms of Hyperbolic Surfaces

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • E. V. Nozdrinova,
  • O. V. Pochinka

摘要

Abstract

We consider a class of gradient-like diffeomorphisms of closed surfaces with negative Euler characteristic. It is shown that all such identity-isotopic diffeomorphisms are connected by a stable arc (containing finitely many saddle-node bifurcations). This result is contrast with the stable classification of gradient-like diffeomorphisms of the 2-sphere or the 2-torus, according to which the set of identity-isotopic diffeomorphisms on such surfaces is divided into a countable number of stable connectivity classes.