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<p>We study planar flows without non-wandering points and prove several properties of these flows in relation with their prolongational relation. With this article we achieve two main results. On one side, we show that planar (regular) wandering flows have only two topological invariants: the space of their orbits and their prolongational relations (or, equivalently, their smallest streams). As a consequence, the result above shows, for the first time in literature, that, as argued recently by James A. Yorke and the second author, streams are a more fundamental concept than recurrence.</p>

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Wandering Flows on the Plane

  • 期刊论文

  • 发表日期：

    2026年2月23日

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  • Joseph Auslander,
  • Roberto De Leo

摘要

We study planar flows without non-wandering points and prove several properties of these flows in relation with their prolongational relation. With this article we achieve two main results. On one side, we show that planar (regular) wandering flows have only two topological invariants: the space of their orbits and their prolongational relations (or, equivalently, their smallest streams). As a consequence, the result above shows, for the first time in literature, that, as argued recently by James A. Yorke and the second author, streams are a more fundamental concept than recurrence.