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Topological Stability for Flows from a Gromov–Hausdorff Viewpoint

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Abstract

In this paper we propose a definition of a distance between flows of possibly different metric spaces. This notion is then combined with the concept of topologically stable flow to obtain the notion of \(\sigma \)-topologically GH-stable flow. Afterwards, we prove that an expansive flow of a compact metric space, with the pseudo-orbit tracing property, and without singularities is \(\sigma \)-topologically GH-stable.

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  1. Instituto de Matemática y Ciencias Afines (IMCA), Universidad Nacional de Ingeniería, Lima, Perú

    Andrés Chulluncuy

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  1. Andrés Chulluncuy
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Correspondence to Andrés Chulluncuy.

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The author was partially supported by FONDECYT from Peru (C.G. 217-2014).

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Chulluncuy, A. Topological Stability for Flows from a Gromov–Hausdorff Viewpoint. Bull Braz Math Soc, New Series 53, 307–341 (2022). https://doi.org/10.1007/s00574-021-00260-x

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  • DOI: https://doi.org/10.1007/s00574-021-00260-x

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