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<p>Linear relations, defined as submodules of the direct sum of two modules, can be viewed as objects that carry dynamical information and reflect the inherent uncertainty of sampled dynamics. These objects also provide an algebraic structure that enables the definition of subtle invariants for dynamical systems. By recognizing specific categorical aspects of these objects, we prove that linear relations defined on modules of finite length are shift equivalent to bijective mappings.</p>

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Linear Relations of Finite Length Modules are Shift Equivalent to Maps

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月20日

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  • Bartosz Furmanek,
  • Filip Oskar Łanecki,
  • Mateusz Przybylski,
  • Jim Wiseman

摘要

Linear relations, defined as submodules of the direct sum of two modules, can be viewed as objects that carry dynamical information and reflect the inherent uncertainty of sampled dynamics. These objects also provide an algebraic structure that enables the definition of subtle invariants for dynamical systems. By recognizing specific categorical aspects of these objects, we prove that linear relations defined on modules of finite length are shift equivalent to bijective mappings.